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| 開催情報 | 水曜日16:40～17:40数理科学研究科棟(駒場) 056号室 |
| 担当者 | 志甫 淳 |
16:40 - 17:40 数理科学研究科棟(駒場) 002号室
梅崎直也 氏 (東京大学数理科学研究科)
『 On uniform bound of the maximal subgroup of the inertia group acting unipotently on $¥ell$-adic cohomology 』(JAPANESE)
For a smooth projective variety over a local field,
the action of the inertia group on the $¥ell$-adic cohomology group is
unipotent if it is restricted to some open subgroup.
In this talk, we give a uniform bound of the index of the maximal open
subgroup satisfying this property.
This bound depends only on the Betti numbers of $X$ and certain Chern
numbers depending on a projective embedding of $X$.
16:40 - 17:40 数理科学研究科棟(駒場) 056号室
Alan Lauder 氏 (University of Oxford)
『 Explicit constructions of rational points on elliptic curves 』(ENGLISH)
I will present an algorithm for computing certain special
values of p-adic L-functions, and discuss an application to
the efficient construction of rational points on elliptic curves.
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
Damian Rossler 氏 (CNRS, Universite de Toulouse)
『 Around the Mordell-Lang conjecture in positive characteristic 』(ENGLISH)
Let V be a subvariety of an abelian variety A over C and let G\subseteq A(C) be a subgroup. The classical Mordell-Lang conjecture predicts that if V is of general type and G\otimesQ is finite dimensional, then V\cap G is not Zariski dense in V. This statement contains the Mordell conjecture as well as the Manin-Mumford conjecture (for curves). The positive characteristic analog of the Mordell-Lang conjecture makes sense, when A is supposed to have no subquotient, which is defined over a finite field. This positive characteristic analog was proven in 1996 by E. Hrushovski using model-theoretic methods. We shall discuss the prehistory and context of this proof. We shall also discuss the proof (due to the speaker) of the fact that in positive characteristic, the Manin-Mumford conjecture implies the Mordell-Lang conjecture (whereas this seems far from true in characteristic 0).
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
18:00 - 19:00 数理科学研究科棟(駒場) 056号室
望月拓郎 氏 (京都大学数理解析研究所)
『 Twistor $D$-module and harmonic bundle 』(ENGLISH)
Abstract:
We shall overview the theory of twistor $D$-modules and
harmonic bundles. I am planning to survey the following topics,
motivated by the Hard Lefschetz Theorem for semisimple holonomic
$D$-modules:
1. What is a twistor $D$-module?
2. Local structure of meromorphic flat bundles
3. Wild harmonic bundles from local and global viewpoints
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
18:15 - 19:15 数理科学研究科棟(駒場) 056号室
Toby Gee 氏 (Imperial College London)
『 New perspectives on the Breuil-Mézard conjecture (joint with M. Emerton) 』(ENGLISH)
I will discuss joint work with Matthew Emerton on geometric approaches to the Breuil-Mézard conjecture, generalising a geometric approach of Breuil and Mézard. I will discuss a proof of the geometric version of the original conjecture, as well as work in progress on a geometric version of the conjecture which does not make use of a fixed residual representation.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
加藤和也 氏 (シカゴ大学)
『 Sharifi 予想について 』(JAPANESE)
円分体の数論とモジュラー曲線の間に深い関係があることは、Mazur と Wiles によって、岩澤主予想の証明に使われた。最近 Sharifi は、更にもう一段深い関係があるということを予想した。これに関する深谷太香子氏との共同研究について述べる。
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
いつもと曜日と部屋が違います。ご注意ください。
Tamas Szamuely 氏 (Budapest)
『 Galois Theory: Past and Present 』(ENGLISH)
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
いつもと時間が異なりますのでご注意ください.
Lucien Szpiro 氏 (City University of New York)
『 Good and bad reduction for algebraic dynamical systems 』(ENGLISH)
We will report on a recent work with collaborators in New York on the
different ways to look at degenerations of a dynamical system in a one
parameter family. Resultants, conductors and isotriviality will be analyzed.
18:30 - 19:30 数理科学研究科棟(駒場) 056号室
曜日,時間がいつもと異なりますのでご注意ください.
Gerd Faltings 氏 (Max Planck Institute for Mathematics, Bonn)
『 Nonabelian p-adic Hodge theory and Frobenius 』(ENGLISH)
Some time ago, I constructed a relation between Higgs-bundles and p-adic etale sheaves, on curves over a p-adic field. This corresponds (say in the abelian case) to a Hodge-Tate picture. In the lecture I try to explain one way to introduce Frobenius into the theory. We do not get a complete theory but at least can treat p-adic sheaves close to trivial.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
18:00 - 19:00 数理科学研究科棟(駒場) 056号室
いつもと時間が異なりますのでご注意下さい.
志甫 淳 氏 (東京大学数理科学研究科)
『 On extension and restriction of overconvergent isocrystals 』(ENGLISH)
First we explain two theorems concerning (log) extension of overconvergent isocrystals. One is a p-adic analogue of the theorem of logarithmic extension of regular integrable connections, and the other is a p-adic analogue of Zariski-Nagata purity. Next we explain a theorem which says that we can check certain property of overconvergent isocrystals by restricting them to curves.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
金城 謙作 氏 (東京大学数理科学研究科)
『 Hypergeometric series and arithmetic-geometric mean over 2-adic fields 』(JAPANESE)
Dwork proved that the Gaussian hypergeometric function on p-adic numbers
can be extended to a function which takes values of the unit roots of
ordinary elliptic curves over a finite field of characteristic p>2.
We present an analogous theory in the case p=2.
As an application, we give a relation between the canonical lift
and the unit root of an elliptic curve over a finite field of
characteristic 2
by using the 2-adic arithmetic-geometric mean.
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。
Andrei Suslin 氏 (Northwestern University)
『 K_2 of the biquaternion algebra 』(ENGLISH)
http://www.ihes.fr/~abbes/SGA/suslin.pdf
16:00 - 18:15 数理科学研究科棟(駒場) 123号室
いつもと時間,教室が異なりますのでご注意下さい.
斎藤毅 氏 (東京大学数理科学研究科) 16:00 - 17:00
『 Discriminants and determinant of a hypersurface of even dimension 』(ENGLISH)
The determinant of the cohomology of a smooth hypersurface
of even dimension as a quadratic character of the absolute
Galois group is computed by the discriminant of the de Rham
cohomology. They are also computed by the discriminant of a
defining polynomial. We determine the sign involved by testing
the formula for the Fermat hypersurfaces.
This is a joint work with J-P. Serre.
Dennis Eriksson 氏 (University of Gothenburg) 17:15 - 18:15
『 Multiplicities of discriminants 』(ENGLISH)
The discriminant of a homogenous polynomial is another homogenous
polynomial in the coefficients of the polynomial, which is zero
if and only if the corresponding hypersurface is singular. In
case the coefficients are in a discrete valuation ring, the
order of the discriminant (if non-zero) measures the bad
reduction. We give some new results on this order, and in
particular tie it to Bloch's conjecture/the Kato-T.Saito formula
on equality of localized Chern classes and Artin conductors. We
can precisely compute all the numbers in the case of ternary
forms, giving a partial generalization of Ogg's formula for
elliptic curves.
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
阿部知行 氏 (東大IPMU)
『 Product formula for $p$-adic epsilon factors 』(ENGLISH)
I would like to talk about my recent work jointly with A. Marmora on a product formula for $p$-adic epsilon factors. In 80's Deligne conjectured that a constant appearing in the functional equation of $L$-function of $\ell$-adic lisse sheaf can be written by means of local contributions, and proved some particular cases. This conjecture was proven later by Laumon, and was used in the Lafforgue's proof of the Langlands' program for functional filed case. In my talk, I would like to prove a $p$-adic analog of this product formula.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
平野雄一 氏 (東京大学数理科学研究科)
『 保型形式の合同式と岩澤λ不変量について 』(JAPANESE)
カスプ形式とEisenstein級数のFourier係数の間の合同式からそれらに付随する L 関数の特殊値の間の合同式を導くという問題を考える。
これは保型形式の重さが 2 の場合はVatsal氏によって証明された。本講演では,重さが 2 以上の場合に一般化できた結果を紹介する。
さらに、この結果を保型形式に付随する p 進Galois表現が剰余して可約という特別な場合の岩澤主予想に応用する。これは、重さが 2 の場合のGreenberg氏及びVatsal氏の結果を部分的に一般化したものである。
17:00 - 18:00 数理科学研究科棟(駒場) 056号室
松本雄也 氏 (東京大学数理科学研究科)
『 On good reduction of some K3 surfaces 』(JAPANESE)
局所体 K 上の多様体がいつ良い還元をもつかを調べる.
多様体 X が良い還元をもつならば,
X の l 進エタールコホモロジーから定まるガロア表現は不分岐表現となる
(ここで l は K の剰余体の標数と異なる素数).
では逆に,このガロア表現が不分岐ならば良い還元をもつか …(*)
という問題を考えると,
X がアーベル多様体ならば (*) は成り立つ(Serre--Tate)が,
一般の多様体では成り立たない.
そこで,(*) が成り立つような多様体のクラスを探すことを考える.
この講演では,ある種の K3 曲面について (*) をやや弱めた主張が成り立つことを紹介する.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
西本将樹 氏 (東京大学数理科学研究科)
『 On the linear independence of values of some Dirichlet series 』(JAPANESE)
周期的な係数を持つDirichlet級数の特殊値が生成する$\Q$線型空間の
次元の下界について,得られた評価を紹介する.
特にこのようなDirichlet級数の偶数または奇数での値に,
無限個の無理数が存在することが分かる.
考えているDirichlet級数がRiemannの$\zeta$関数のときは,同様の結果が
2000年にT.Rivoalにより証明されており,今回の結果はその一般化に相当する.
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
Michel Raynaud 氏 (Universite Paris-Sud)
『 Permanence following Temkin 』(ENGLISH)
When one proceeds to a specialization, the good properties of algebraic equations may be destroyed. Starting with a bad specialization, one can try to improve it by performing modifications under control. If, at the end of the process, the initial good properties are preserved, one speaks of permanence. I shall give old and new examples of permanence. The new one concerns the relative semi-stable reduction of curves recently proved by Temkin.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
高井勇輝 氏 (東京大学数理科学研究科)
『 Sturm の定理の Hilbert 保型形式に対する類似 』(JAPANESE)
Sturm は重さ$k$, レベル$\Gamma_1(N)$ のmod $\ell$ 正則楕円保型形式が最初
の$(k/12)[\Gamma_1(1):\Gamma_1(N)]$ までの mod $\ell$ Fourier 係数で決ま
ることを示した.
本講演では, Sturm の結果のHilbert保型形式に対する類似について得た結果を
紹介する.
証明には代数幾何的な手法, 特に, ampleな線束のpositivityを用いる.
11:00 - 12:00 数理科学研究科棟(駒場) 056号室
曜日・時間がいつもと異なりますのでご注意ください.
Joseph Ayoub 氏 (University of Zurich)
『 The motivic Galois group and periods of algebraic varieties 』(ENGLISH)
We give a construction of the motivic Galois group of $\Q$ and explain the conjectural link with the ring of periods of algebraic varieties. Then we introduce the ring of formal periods and explain how the conjectural link with the motivic Galois group can be realized for them.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
小林真一 氏 (東北大学)
『 楕円曲線の超特異素点におけるp-進Gross-Zagier公式 』(JAPANESE)
p進Gross-Zagier公式は, 楕円曲線のp進L関数の微分値をHeegner点のp進高さで記述する公式である. 楕円曲線がpで通常還元をもつときは, 20年以上前にPerrin-Riouによって証明されていた. 最近, pで超特異還元をもつときにも証明できたのでそれを紹介する. この講演では特に証明の解説に重点をおいて話したい.
16:30 - 18:45 数理科学研究科棟(駒場) 056号室
Zhonghua Li 氏 (東京大学大学院数理科学研究科) 16:30 - 17:30
『 On regularized double shuffle relation for multiple zeta values 』(ENGLISH)
Multiple zeta values(MZVs) are natural generalizations of Riemann zeta values. There are many rational relations among MZVs. It is conjectured that the regularized double shuffle relations contian all rational relations of MZVs. So other rational relations should be deduced from regularized dhouble shuffle relations. In this talk, we discuss some results on this problem. We define the gamma series accociated to elements satisfying regularized double shuffle relations and give some properties. Moreover we show that the Ohno-Zagier relations can be deduced from regularized double shuffle relations.
Dan Yasaki 氏 (North Carolina University) 17:45 - 18:45
『 Spines with View Toward Modular Forms 』(ENGLISH)
The study of an arithmetic group is often aided by the fact that it acts naturally on a nice topological object. One can then use topological or geometric techniques to try to recover arithmetic data. For example, one often studies SL_2(Z) in terms of
its action on the upper half plane. In this talk, we will examine spines, which are the ``smallest" such spaces for a given arithmetic group. On overview of some known theoretical results and explicit computations will be given.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
原隆 氏 (東京大学大学院数理科学研究科)
『 総実代数体の羃指数p型非可換p拡大に対するp-進ゼータ関数の帰納的構成 』(JAPANESE)
総実代数体の非可換岩澤理論に於けるp-進ゼータ関数の構成及び
主予想の証明について、特別な場合に解説する。
総実代数体の非可換岩澤主予想は、David Burns 及び加藤和也による
「ゼータ関数の貼り合わせ」の手法を用いて加藤、Mahesh Kakde 及び
講演者によって特別な場合に証明されてきた (Jurgen Ritter,
Alfred Weiss も異なる定式化の下で主予想が成立する例を構成している)。
本講演では拡大のガロワ群がp進整数環と羃指数pの有限群の直積と
同型の場合に、Burns-加藤の手法と帰納的な議論を組み合わせることで
非可換岩澤主予想が証明できることを紹介する。
なお、総実代数体の非可換岩澤主予想は、2010年に
Ritter-Weiss 及び Kakde によって一般の場合にも
解決されていることを注記しておく。
16:30 - 18:45 数理科学研究科棟(駒場) 056号室
星裕一郎 氏 (京都大学数理解析研究所) 16:30 - 17:30
『 On a problem of Matsumoto and Tamagawa concerning monodromic fullness of hyperbolic curves 』(JAPANESE)
In this talk, we will discuss the following problem posed by Makoto Matsumoto and Akio Tamagawa concerning monodromic fullness of hyperbolic curves.
For a hyperbolic curve X over a number field, are the following three conditions equivalent?
(A) For any prime number l, X is quasi-l-monodromically full.
(B) There exists a prime number l such that X is l-monodromically full.
(C) X is l-monodromically full for all but finitely many prime numbers l.
The property of being (quasi-)monodromically full may be regarded as an analogue for hyperbolic curves of the property of not admitting complex multiplication for elliptic curves, and the above equivalence may be regarded as an analogue for hyperbolic curves of the following result concerning the Galois representation on the Tate module of an elliptic curve over a number field proven by Jean-Pierre Serre.
For an elliptic curve E over a number field, the following four conditions are equivalent:
(0) E does not admit complex multiplication.
(1) For any prime number l, the image of the l-adic Galois representation associated to E is open.
(2) There exists a prime number l such that the l-adic Galois representation associated to E is surjective.
(3) The l-adic Galois representation associated to E is surjective for all but finitely many prime numbers l.
In this talk, I will present some results concerning the above problem in the case where the given hyperbolic curve is of genus zero. In particular, I will give an example of a hyperbolic curve of type (0,4) over a number field which satisfies condition (C) but does not satisfy condition (A).
Marco Garuti 氏 (University of Padova) 17:45 - 18:45
『 Galois theory for schemes 』(ENGLISH)
We discuss some aspects of finite group scheme actions: the Galois correspondence and the notion of Galois closure.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
原瀬 晋 氏 (東京大学大学院数理科学研究科)
『 F_2-線形擬似乱数発生法の評価に用いる格子の簡約基底計算の高速化 』(JAPANESE)
(部分的に松本眞氏、斎藤睦夫氏との共同研究)
擬似乱数発生法とは、あたかも乱数であるかのようにふるまう数列を、計算機上で
決定的なアルゴリズムにより発生する方法のことである。擬似乱数を評価する規準
の一つとして、高次元均等分布性がしばしば用いられる。メルセンヌツイスター法
を含む二元体上の線形擬似乱数発生法に対しては、上位ビットの均等分布の次元を
具体的に計算することが可能であり、擬似乱数の出力列から構成したある格子の簡
約基底を求める問題(二元体係数形式的冪級数体の数の幾何)に帰着される(Couture-
L'Ecuyer-Tezuka(1993)およびTezuka(1994))。本研究では、前述の格子を用いた
計算法を発展させ、
(i) 冪級数成分の格子点を擬似乱数発生器の状態ベクトルで表現する、
(ii) 射影を用いてv次元簡約基底からv-1次元簡約基底を計算する、
(iii) 効率的な格子簡約アルゴリズムを適用する、
などの手法を導入し、均等分布の次元計算の高速化を提案する。この方法は、
Couture-L'Ecuyer(2000)による双対格子を用いた改良よりも計算量が少なく、計算機
実験でも10倍程度の高速化が得られたことを紹介する。この結果は、ワードサイズの
大きな擬似乱数発生法の設計や擬似乱数の並列発生スキームなどへの応用が考えられる。
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
いつもと教室が異なりますのでご注意ください
Hélène Esnault 氏 (Universität Duisburg-Essen)
『 Finite group actions on the affine space 』(ENGLISH)
If $G$ is a finite $\ell$-group acting on an affine space $\A^n$ over a
finite field $K$ of cardinality prime to $\ell$, Serre shows that there
exists a rational fixed point. We generalize this to the case where $K$ is a
henselian discretely valued field of characteristic zero with algebraically
closed residue field and with residue characteristic different from $\ell$.
We also treat the case where the residue field is finite of cardinality $q$
such that $\ell$ divides $q-1$. To this aim, we study group actions on weak
N\'eron models.
(Joint work with Johannes Nicaise)
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
津嶋 貴弘 氏 (東京大学数理科学研究科)
『 On the stable reduction of $X_0(p^4)$ 』(JAPANESE)
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
Luc Illusie 氏 (Universite de Paris-Sud)
『 Vanishing theorems revisited, after K.-W. Lan and J. Suh 』(ENGLISH)
Let k be an algebraically closed field of characteristic p and X,
Y proper, smooth k-schemes. J. Suh has proved a vanishing theorem of Kollar
type for certain nef and big line bundles L on Y and morphisms f : X -> Y
having semistable reduction along a divisor with simple normal crossings. It
holds both if p = 0 and if p > 0 modulo some additional liftability mod p^2
and dimension assumptions, and generalizes vanishing theorems of Esnault-
Viehweg and of mine. I'll give an outline of the proof and sketch some
applications, due to K.-W. Lan and J. Suh, to the cohomology of certain
automorphic bundles arising from PEL type Shimura varieties.
16:15 - 17:15 数理科学研究科棟(駒場) 052号室
Richard Hain 氏 (Duke大学)
『 Universal mixed elliptic motives 』(ENGLISH)
This is joint work with Makoto Matsumoto. A mixed elliptic
motive is a mixed motive (MHS, Galois representation, etc) whose
weight graded quotients are Tate twists of symmetric powers of the the
motive of elliptic curve. A universal mixed elliptic motive is an
object that can be specialized to a mixed elliptic motive for any
elliptic curve and whose specialization to the nodal cubic is a mixed
Tate motive. Universal mixed elliptic motives form a tannakian
category. In this talk I will define universal mixed elliptic motives,
give some fundamental examples, and explain what we know about the
fundamental group of this category. The "geometric part" of this group
is an extension of SL_2 by a prounipotent group that is generated by
Eisenstein series and which has a family of relations for each cusp
form. Although these relations are not known, we have a very good idea
of what they are, thanks to work of Aaron Pollack, who determined
relations between the generators in a very large representation of
this group.
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
Fabrice Orgogozo 氏 (CNRS, École polytechnique)
『 エタールコホモロジーの高次順像の一様構成可能性について 』(ENGLISH)
Z_ℓエタールコホモロジーの捻れとF_ℓコホモロジーの超積の関係を巡り
N. Katz氏の指摘に基づいて、高次順像に於けるℓに対する
一様構成可能性についての定理を証明する。
(この様な定理は以前よりガバー氏の構想に有った。)
ここでは月並みな方法で有るが、A.J.de Jong氏の定理と
少量の対数的幾何学を使う。
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
富安亮子 氏 (高エネルギー加速器研究機構)
『 On some algebraic properties of CM-types of CM-fields and their reflex fields 』(JAPANESE)
Shimura and Taniyama proved in their theory of complex
multiplication that the moduli of abelian varieties of a CM-type and their
torsion points generate an abelian extension, not of the field of complex
multiplication, but of a reflex field of the field. In this talk, I
introduce some algebraic properties of CM-types, half norm maps that might
shed new light on reflex fields.
For a CM-field $K$ and its Galois closure $K^c$ over the rational field $Q$,
there is a canonical embedding of $Gal (K^c/Q)$ into $(Z/2Z)^n \rtimes S_n$.
Using properties of the embedding, a set of CM-types $\Phi$ of $K$ and their
dual CM-types $(K, \Phi)$ is equipped with a combinatorial structure. This
makes it much easier to handle a whole set of CM-types than an individual
CM-type.
I present a theorem that shows the combinatorial structure of the dual
CM-types is isomorphic to that of a Pfister form.
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
松本 眞 氏 (東京大学数理科学研究科)
『 Differences between Galois representations in outer-automorphisms of the fundamental groups and those in automorphisms, implied by topology of moduli spaces 』(ENGLISH)
Fix a prime l. Let C be a proper smooth geometrically connected curve over a number field K, and x be its closed point. Let Π denote the pro-l completion of the geometric fundamental group of C with geometric base point over x. We have two non-abelian Galois representations:
ρA : Galk(x) → Aut(Π),ρO : GalK → Out(Π).
Our question is: in the natural inclusion Ker(ρA) ⊂ Ker(ρO) ∩ Galk(x), whether the equality holds or not. Theorem: Assume that g ≥ 3, l divides 2g -2. Then, there are infinitely many pairs (C, K) with the following property. If l does not divide the extension degree [k(x): K], then Ker(ρA) = (Ker(ρO) ∩ Galk(x)) holds.
This is in contrast to the case of the projective line minus three points and its canonical tangential base points, where the equality holds (a result of Deligne and Ihara).
There are two ingredients in the proof: (1) Galois representations often contain the image of the geometric monodromy (namely, the mapping class group) [M-Tamagawa 2000] (2) A topological result [S. Morita 98] [Hain-Reed 2000] on the cohomological obstruction of lifting the outer action of the mapping class group to automorphisms.
(This lecture is held as `Arithmetic Geometry Seminar Tokyo-Paris' and it is transmitted to IHES by the internet.)
17:30 - 18:30 数理科学研究科棟(駒場) 056号室
Gerard Laumon 氏 (CNRS, Universite Paris XI - Orsay)
『 The cohomological weighted fundamental lemma 』
Using the Hitchin fibration, Ngo Bao Chau has proved the Langlands-Shelstad fundamental lemma. In a joint work with Pierre-Henri Chaudouard, we have extended Ngo's proof to obtain the weighted fundamental lemma which had been conjectured by Arthur. In the talk, I would like to present our main cohomological result.
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
16:30 - 18:45 数理科学研究科棟(駒場) 056号室
津嶋 貴弘 氏 (東京大学大学院数理科学研究科) 16:30 - 17:30
『 Elementary computation of ramified component of the Jacobi sum 』
R. Coleman and W. McCallum calculated the Jacobi sum Hecke characters using their computation of the stable reduction of the Fermat curve in 1988. In my talk, we give an elementary proof of the main result of them without using rigid geometry or the stable model of the Fermat curve.
Christopher Deninger 氏 (Universität Münster) 17:45 - 18:45
『 P-divisible groups and the p-adic Corona problem 』
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
Bernard Le Stum 氏 (Université de Rennes 1)
『 The local Simpson correspondence in positive characteristic 』
A Simpson correspondance should relate Higgs bundles to differential modules (or local systems). We stick here to positive characteristic and recall some old and recent results : Cartier isomorphism, Van der Put's classification, Kaneda's theorem and Ogus-Vologodsky local theory. We'll try to explain how the notion of Azumaya algebra is a convenient tool to unify these results. Our main theorem is the equivalence between quasi-nilpotent differential modules of level m and quasi-nilpotent Higgs Bundles (depending on a lifting of Frobenius mod p-squared). This result is a direct generalization of the previous ones. The main point is to understand the Azumaya nature of the ring of differential operators of level m. Following Berthelot, we actually use the dual theory and study the partial divided power neighborhood of the diagonal.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
Ahmed Abbes 氏 (Université de Rennes 1)
『 On GAGA theorems for the rigide-étale topology 』
Last year, I finished my course in Todai on "Rigide Geometry following M. Raynaud" by stating a GAGA theorem for the rigide-étale topology, due to Gabber and Fujiwara. I will give a new proof of this theorem, inspired by another theorem of Gabber, namely the Affine analog of the proper base change theorem.
11:00 - 12:00 数理科学研究科棟(駒場) 123号室
いつもと、曜日、時間、教室が違います。
午後からは、織田先生還暦記念の研究集会がはじまります。
Dinakar Ramakrishnan 氏 (カリフォルニア工科大学)
『 Modular forms and Calabi-Yau varieties 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
いつもと曜日が違います。
Fabien Trihan 氏 (Nottingham大学)
『 On the $p$-parity conjecture in the function field case 』
Let $F$ be a function field in one variable with field of constant a finite field of characteristic $p>0$. Let $E/F$ be an elliptic curve over $F$. We show that the order of the Hasse-Weil $L$-function of $E/F$ at $s=1$ and the corank of the $p$-Selmer group of $E/F$ have the same parity (joint work with C. Wuthrich).
16:30 - 18:45 数理科学研究科棟(駒場) 056号室
Vincent Maillot 氏 (Paris第7大学) 16:30 - 17:30
『 New algebraicity results for analytic torsion 』
Richard Hain 氏 (Duke大学) 17:45 - 18:45
『 On the Section Conjecture for the universal curve over function fields 』
16:30 - 18:30 数理科学研究科棟(駒場) 056号室
Bruno Kahn 氏 (Paris第7大学)
『 On the classifying space of a linear algebraic group 』
16:30 - 18:30 数理科学研究科棟(駒場) 056号室
Bruno Kahn 氏 (Paris第7大学)
『 Motives and adjoints 』
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
Gombodorj Bayarmagnai 氏 (東京大学大学院数理科学研究科)
『 The (g,K)-module structure of principal series and related Whittaker functions of SU(2,2) 』
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
廣江 一希 氏 (東京大学大学院数理科学研究科)
『 Generalized Whittaker functions for degenerate principal series of GL(4,R) 』
16:30 - 18:45 数理科学研究科棟(駒場) 056号室
大久保 俊 氏 (東京大学大学院数理科学研究科) 16:30 - 17:30
『 剰余体が非完全な場合のB_dR^+のGalois理論 』
斎藤 秀司 氏 (東京大学大学院数理科学研究科) 17:45 - 18:45
『 A counterexample of Bloch-Kato conjecture over a local field and infinite torsion in algebraic cycles of codimension two 』
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
Pierre Colmez 氏 (École polytechnique)
『 On the p-adic local Langlands correspondence 』
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
鈴木正俊 氏 (東京大学大学院数理科学研究科)
『 Mean-periodicity and analytic properties of zeta-functions 』
Mean-periodicityというのは周期性の概念のひとつの一般化である。最近、I. Fesenko, G. Ricottaとの共同研究により、数論的スキームのゼータ関数を含むある複素関数のクラスと、mean-periodicityとの関連性が新しく見出された。
これはHecke-Weilによる, 解析接続と関数等式を持つDirichlet級数と保型形式との対応の一つの拡張ともみなせる. この背景には, I. Fesenkoの高次元アデール上のゼータ積分の理論があり、数論的スキームのHasseゼータ関数の解析接続を高次元アデール上の調和解析から導こうというプログラムの一環となっている。
この講演ではそのような背景にも若干触れた上、ゼータ関数の解析的性質とmean-periodicityの関連、特に解析接続と関数等式との関連について解説する。
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
平田典子 氏 (日本大学理工学部)
『 Lang's Observation in Diophantine Problems 』
In 1964, Serge Lang suggested the following problem, which reads now as follows:
Let $E$ be an elliptic curve defined over a number field $K$, and $\varphi$ be a rational function on $E$. Then, for every point $P\in E(K)$ where $\varphi$ does not vanish at $P$, the logarithms of a norm of $\varphi(P)$ is at worst linear in the logarithms of the Neron-Tate height of the point $P$.
We give a simultaneous Diophantine approximation for linear forms in elliptic logarithms which actually implies this conjecture. We also present Lang's observations in Diophantine problems.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
Olivier Fouquet 氏 (大阪大学)
『 Dihedral Iwasawa theory of ordinary modular forms 』
According to Hida theory, the Galois representation attached to a nearly-ordinary Hilbert eigencuspform belongs to a p-adic analytic family of Galois representations parametrized by varying weights. After restricting it to the absolute Galois group of a quadratic totally complex extension, it also belongs to a p-adic family coming from classical dihedral Iwasawa theory. We will explain the proofs of part of the main conjecture in Iwasawa theory in these situations, i.e divisibilities of characteristic ideals when equalities are actually expected.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
Daniel Caro 氏 (Université de Caen)
『 Overholonomicity of overconvergence $F$-isocrystals on smooth varieties 』
Let $¥mathcal{V}$ be a complete discrete valuation ring
of characteristic $0$, with perfect residue field $k$ of
characteristic $p>0$. In order to construct $p$-adic coefficients
over $k$-varieties, Berthelot introduced the theory of
overconvergent $F$-isocrystals, i.e overconvergent isocrystals with
Frobenius structure. Moreover, to get a $p$-adic cohomology over
$k$-varieties stable under cohomological operations, Berthelot built
the theory of arithmetic $F$-$¥mathcal{D}$-modules. In this talk,
after recalling some elements of these theories, we introduce the
notion of overholonomicity with is a property as stable as the
holonomicity in the classical theory of $¥mathcal{D}$-modules. The
goal of the talk is to prove the overholonomicity of arithmetic
$¥mathcal{D}$-modules associated to overconvergent $F$-isocrystals
over smooth $k$-varieties. In the proof we need Christol's transfert
theorem, a comparison theorem between relative log rigid cohomology
and relative rigid cohomology and last but not least Kedlaya's
semistable reduction theorem. This is a joint work with Nobuo
Tsuzuki.
16:30 - 17:30 数理科学研究科棟(駒場) 056号室
10月から教室が056号室に変更になります.
Pierre Parent 氏 (Universite Bordeaux 1)
『 Serre's uniformity in the split Cartan case 』
We show that, for large enough prime number p, the modular curve
X_{split}(p) has no other point with values in Q than CM points and the rational cusp. This gives a partial answer to an old question of J.-P. Serre concerning the uniform surjectivity of Galois representations associated to torsion points on elliptic curves without complex multiplication.
(Joint work with Yuri Bilu.)
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
いつもと曜日が異なりますのでご注意下さい.
Christopher Deninger 氏 (Munster大学)
『 A determinant for p-adic group algebras 』
For a discrete countable group G there is a classical determinant on the units of the L^1-convolution algebra of G. It is defined using functional analysis and can be used for example to calculate the entropy of certain G-actions. We will discuss a p-adic analogue of this theory. Instead of functional analysis the definition of the p-adic determinant uses algebraic K-theory. It has an application to the study of the p-adic distribution of periodic G-orbits in certain G-action.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Don Zagier 氏 (Max Planck研究所)
『 $q$-series and modularity 』
13:00 - 18:00 数理科学研究科棟(駒場) 002号室
4講演あります.また,いつもと曜日,時間,場所が異なります.
ご注意下さい.
Olivier Brinon 氏 (Paris北大学) 13:00 - 14:00
『 B_dR-representations and Higgs bundles 』
Henrik Russell 氏 (Duisburg-Essen大学) 14:15 - 15:15
『 Generalized Albanese and duality 』
Thomas Geisser 氏 (南California大学) 15:45 - 16:45
『 Negative K-theory, homotopy invariance and regularity 』
The topic of my talk are two classical conjectures in K-theory:
Weibel's conjecture states that a scheme of dimension d
has no K-groups below degree -d, and Vorst's conjecture
states that homotopy invariance of the K-theory of rings
implies that the ring must be regular.
I will give an easy introduction to the conjectures, and discuss
recent progress.
Fabien Trihan 氏 (Nottingham大学) 17:00 - 18:00
『 On Iwasawa theory for abelian varieties over function fields of positive characteristic 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Valentina Di Proietto 氏 (Padova大学)
『 On p-adic differential equation on semi-stable varieties 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
近藤 智 氏 (東京大学数物連携宇宙研究機構)
『 有限体上のスキームのふたつのモチビックコホモロジー群の計算 (安田正大氏との共同研究) 』
16:30 - 18:45 数理科学研究科棟(駒場) 117号室
服部 新 氏 (北海道大学大学院理学研究院) 16:30 - 17:30
『 On a ramification bound of semi-stable torsion representations over a local field 』
朝倉 政典 氏 (北海道大学大学院理学研究院) 17:45 - 18:45
『 Beilinson-Tate予想と楕円曲面のK_1の不分解元 』
(佐藤周友氏との共同研究)
代数サイクルのTate予想のK理論における類似であるBeilinson-Tate予想について、
楕円曲面の場合にそれが成り立つ非自明な例を構成する。
これは、p進レギュレーターの非消滅と関係しており、
応用としてK_1の不分解元であって整数環上のモデルからくるようなものを構成する。
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
坂内 健一 氏 (慶應義塾大学理工学部 )
『 $p$-adic elliptic polylogarithm, $p$-adic Eisenstein series and Katz measure (joint work with G. Kings) 』
The Eisenstein classes are important elements in the motivic cohomology
of a modular curve, defined as the specializations of the motivic elliptic
polylogarithm by torsion sections. The syntomic Eisenstein classes are
defined as the image by the syntomic regulator of the motivic Eisenstein
classes. In this talk, we explain our result concerning the relation between
syntomic Eisenstein classes restricted to the ordinary locus and
p-adic Eisenstein series.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
今井 直毅 氏 (東京大学大学院数理科学研究科)
『 On the connected components of moduli spaces of finite flat models 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
原 隆 氏 (東京大学大学院数理科学研究科)
『 Iwasawa theory of totally real fields for certain non-commutative $p$-extensions 』
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Luc Illusie 氏 (Universite Paris-Sud 11)
『 Odds and ends on finite group actions and traces 』
Suppose a finite group G acts on a scheme X separated and of finite type over a field k. This raises several questions about the traces of elements s of G (or more generally products sg, for g in the Galois group of k) on cohomology groups of various types associated with X/k (with compact support or no support, Betti if k = C, l-adic, rigid). Some were considered and solved long ago, others only recently. I will in particular discuss an equivariant generalization of a theorem of Laumon on Euler-Poincar¥'e characteristics.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Weizhe Zheng 氏 (Universite Paris-Sud 11)
『 Integrality, Rationality, and Independence of l in l-adic Cohomology over Local Fields 』
I will discuss two problems on traces in l-adic cohomology over local fields with finite residue field. In the first part, I will describe the behavior of integral complexes of l-adic sheaves under Grothendieck's six operations and the nearby cycle functor. In the second part, I will talk about rationality and independence of l. More precisely, I will introduce a notion of compatibility for systems of l-adic complexes and explain the proof of its stability by the above operations, in a slightly more general context (equivariant under finite groups). The main tool in this talk is a theorem of de Jong on
alterations.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Antoine Chambert-Loir 氏 (Universite de Rennes 1)
『 Equidistribution theorems in Arakelov geometry 』
The proof of Bogomolov's conjecture by Zhang made a crucial use
of an equidistribution property for the Galois orbits of points of small
heights in Abelian varieties defined over number fields.
Such an equidistribution property is proved using a method invented
by Szpiro, Ullmo and Zhang, and makes use of Arakelov theory.
This equidistribution theorem takes place in the complex torus
associated to the Abelian variety. I will show how a similar
equidistribution theorem can be proven for the p-adic topology ;
we have to use Berkovich space. Thanks to recent results of Yuan
about `big line bundles' in Arakelov geometry, the situation
is now very well understood.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
中村健太郎 氏 (東京大学大学院数理科学研究科)
『 Classification of two dimensional trianguline representations of p-adic fields 』
Trianguline representation is a class of p-adic Galois representations of p-adic fields. This was defined by P.Colmez by using ($\varphi, \Gamma$)-modules over Robba ring. In his study of p-adic local Langlands correspondence of GL_2(Q_p), he completely classified two dimensional trianguline representations of Q_p. On the other hand, L.Berger recently defined the category of B-pairs and established the equivalence between the category of B-pairs and the category of ($\varphi,\Gamma$)-modules over Robba ring. In this talk, we extend the Colmez's result by using B-pairs. We completely classify two dimensional trianguline representations of K for any finite extension of Q_p. We also talk about a relation between two dimensional trianguline representations and principal series or special series of GL_2(K).
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Christopher Rasmussen 氏 (京都大学数理解析研究所)
『 Abelian varieties with constrained torsion 』
The pro-$l$ Galois representation attached to the arithmetic fundamental group of a curve $X$ is heavily influenced by the arithmetic of certain classes of its branched covers. It is natural, therefore, to search for and classify these special covers in a meaningful way. When $X$ is the projective line minus three points, one finds that such covers are very scarce. In joint work with Akio Tamagawa, we formulate a conjecture to quanitify this scarcity, and present a proof for the conjecture in the case of genus one curves defined over $\Q$.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Pierre Colmez 氏 (Ecole Polytechnique)
『 On the p-adic local Langlands correspondance for GL2(Qp) 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
阿部知行 氏 (東京大学大学院数理科学研究科)
『 l進層のSwan導手とunit-root overconvergent F-isocrystalの特性サイクルについて 』
今回の講演ではBerthelotによる数論的D加群の理論を用いることによってunit-root overconvergent F-isocrystalに対してSwan導手を定義し、Kato-Saitoにより幾何学的な手法を用いて定義されたSwan導手と比較する。応用として、特異点の解消の仮定のもとでKato-SaitoのSwan導手の整数性予想を導く。
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
代数幾何学セミナーとの合同講演会です
James Lewis 氏 (University of Alberta)
『 Abel-Jacobi Maps Associated to Algebraic Cycles I 』
This talk concerns the Bloch cycle class map from the higher Chow groups to Deligne cohomology of a projective algebraic manifold. We provide an explicit formula for this map in terms of polylogarithmic type currents.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Gereon Quick 氏 (Universitaet Muenster)
『 Etale cobordism 』
We define and study a new candidate of etale topological cohomology theories for schemes over a field of abritrary characteristic: etale cobordism. As etale K-theory is related to algebraic K-theory, etale cobordism is related to algebraic cobordism of Voevodsky and Levine/Morel. It shares some nice properties of topological theories, e.g. it is equipped with an Atiyah-Hirzebruch spectral sequence from etale cohomology. We discuss in particular a comparison theorem between etale and algebraic cobordism after inverting a Bott element and, finally, we give an outlook to further possible applications of this theory.
15:00 - 18:00 数理科学研究科棟(駒場) 117号室
代数幾何学セミナーとの合同講演会です
E. Lau 氏 (Univ. of Bielefeld) 15:00 - 15:45
『 Classification of p-divisible groups by displays and duality 』
T. Zink 氏 (Univ. of Bielefeld) 16:00 - 16:45
『 Applications of the theory of displays 』
E. Looijenga 氏 (Univ. of Utrecht) 17:00 - 18:00
『 Presentation of mapping class groups from algebraic geometry 』
A presentation of the mapping class group of a genus g surface with one hole is due to Wajnryb with later improvements due to M. Matsumoto. The generators are Dehn twists defined by 2g+1 closed curves on the surface. The relations involving only two Dehn twists are the familiar Artin relations, we show that those involving more than two can be derived from algebro-geometry considerations.
16:30 - 17:30 数理科学研究科棟(駒場) 002号室
Steven Zucker 氏 (Johns Hopkins大学)
『 The reductive Borel-Serre motive 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
梶原 健 氏 (横浜国立大学)
『 Tropical toric varieties 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Andreas Rosenschon 氏 (University of Alberta)
『 Algebraic cycles on products of elliptic curves over p-adic fields 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
Stephen Lichtenbaum 氏 (Brown University)
『 The conjecture of Birch and Swinnerton-Dyer is misleading 』
All values of zeta and L-functions at integral points should be given in terms of products and quotients of Euler characteristics, and the order of the zeroes and poles at these
points should be given by the sum and difference of the ranks of
corresponding finitely generated abelian groups.
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
宮崎 直 氏 (東京大学大学院数理科学研究科)
『 $(g,K)$-module structures of principal series representations of $Sp(3,R)$ 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
長谷川 泰子 氏 (東京大学大学院数理科学研究科)
『 Cohen-Eisenstein series and modular forms associated to imaginary quadratic fields 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
津嶋 貴弘 氏 (東京大学大学院数理科学研究科)
『 Localized Characteristic Class and Swan Class 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
斎藤 毅 氏 (東京大学大学院数理科学研究科)
『 l進層の暴分岐と特性サイクル 』
15:15 - 18:45 数理科学研究科棟(駒場) 117号室
3講演です
Dennis Eriksson 氏 (東大数理/Paris) 15:15 - 16:15
『 Towards a proof of a metrized Deligne-Riemann-Roch theorem 』
小林 真一 氏 (名古屋大学多元数理) 16:30 - 17:30
『 CM楕円曲線の超特異点における2変数p進L関数 (A two variable p-adic L-function for CM elliptic curves at supersingular primes) 』
Frans Oort 氏 (Utrecht) 17:45 - 18:45
『 Irreducibility of strata and leaves in the moduli space of abelian varieties 』
16:30 - 18:45 数理科学研究科棟(駒場) 117号室
2講演です
Anna Cadoret 氏 (RIMS/JSPS) 16:30 - 17:30
『 On the profinite regular inverse Galois problem 』
Given a field $k$ and a (pro)finite group $G$, consider the
following weak version of the regular inverse Galois problem:
(WRIGP/$G$/$k$) \textit{there exists a smooth geometrically
irreducible curve $X_{G}/k$ and a Galois extension $E/k(X_{G})$
regular over $k$ with group $G$.} (the regular inverse Galois
problem (RIGP/$G$/$k$) corresponding to the case
$X_{G}=\mathbb{P}^{1}_{k}$). A standard descent argument shows that
for a finite group $G$ the (WRIGP/$G$/$k$) can be deduced from the
(RIGP/$G$/$k((T))$). For
profinite groups $G$, the (WRIGP/$G$/$k((T))$) has been proved for
lots of fields (including the cyclotomic closure of characteristic $0$
fields) but the descent argument no longer works.\
\indent Let $p\geq 2$ be a prime, then a profinite group
$G$ is said to be \textit{$p$-obstructed} if it fits in a profinite group extension
$$1\rightarrow K\rightarrow G\rightarrow G_{0}\rightarrow 1$$
with $G_{0}$ a finite group and $K\twoheadrightarrow
\mathbb{Z}_{p}$. Typical examples of such profinite groups $G$ are
universal $p$-Frattini covers of finite $p$-perfect groups or
pronilpotent projective groups.\
\indent I will show that the (WRIGP/$G$/$k$) - even under
its weaker formulation: (WWRIGP/$G$/$k$) \textit{there exists a
smooth geometrically irreducible curve $X_{G}/k$ and a Galois
extension $E/k(X_{G}).\overline{k}$ with group $G$ and field of
moduli $k$.} - fails for the whole class of $p$-obstructed profinite
groups $G$ and any field $k$ which is either a finitely generated
field of characteristic $0$ or a finite field of characteristic
$\not= p$.\
\indent The proof uses a profinite generalization of the cohomological obstruction
for a G-cover to be defined over its field of moduli and an analysis of the constrainsts
imposed on a smooth geometrically irreducible curve $X$ by a degree $p^{n}$
cyclic G-cover $X_{n}\rightarrow X$, constrainsts which are too rigid to allow the
existence of projective systems $(X_{n}\rightarrow
X_{G})_{n\geq 0}$ of degree $p^{n}$ cyclic G-covers
defined over $k$. I will also discuss other implicsations of these constrainsts
for the (RIGP).
Eric Friedlander 氏 (Northwestern) 17:45 - 18:45
『 An elementary perspective on modular representation theory 』
16:30 - 18:45 数理科学研究科棟(駒場) 117号室
2講演です
Vincent Maillot 氏 (Jussieu/京大数理研) 16:30 - 17:30
『 New applications of the arithmetic Riemann-Roch theorem 』
Don Blasius 氏 (UCLA) 17:45 - 18:45
『 Zariski Closures of Automorphic Galois Representations 』
16:30 - 18:45 数理科学研究科棟(駒場) 117号室
2講演です
G.Bayarmagnai 氏 (東大数理) 16:30 - 17:30
『 Essential dimension of some finite group schemes 』
Jacques Tilouine 氏 (パリ北大学) 17:45 - 18:45
『 Overconvergent Siegel modular forms 』
We recall what is known and what is conjectured on p-adic families of overconvergent Siegel modular forms. We show how this relates to a Fontaine-Mazur type conjecture on the classicality of certain overconvergent Siegel forms of genus 2. We explain few results known in this direction.
17:00 - 18:00 数理科学研究科棟(駒場) 117号室
いつもと時間が違います
平之内 俊郎 氏 (九州大学)
『 Extensions of truncated discrete valuation rings ( 田口雄一郎先生との共同研究 ) 』
局所体の拡大とその付値環の或る商である"truncated" dvrの拡大の圏を比較する. 不分岐拡大と剰余体の拡大が一対一対応するのと同じ様に, 分岐に関する条件を加えれば,局所体と "truncated" dvr の拡大の圏が同値になる (Deligne).
今回は, 古典的な(上付き)分岐群の代わりにAbbes-斎藤による分岐群を用いて分岐に関する条件を与える. そして,この分岐群の Rigid 幾何的解釈を踏襲する事でDeligneの定理の剰余体が非完全な場合への一般化が得られる事を述べる.
16:30 - 18:45 数理科学研究科棟(駒場) 117号室
2講演です
Fabrice Orgogozo 氏 (東大数理・Ecole Polytechnique de Paris) 16:30 - 17:30
『 p-dimension of henselian fields: an application of Ofer Gabber's algebraization technique 』
Kim Minhyong 氏 (Purdue大学・京大数理研) 17:45 - 18:45
『 Fundamental groups and Diophantine geometry 』
16:30 - 17:30 数理科学研究科棟(駒場) 128号室
代数幾何セミナーと共催です
Bas Edixhoven 氏 (Univ. of Leiden)
『 Computation of the mod l Galois representations associated to Delta 』
16:30 - 17:30 数理科学研究科棟(駒場) 128号室
いつもと曜日・部屋ともに違います
A. Marmora 氏 (パリ北大・東大/学振)
『 p-adic local constants 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
桜井 真 氏 (東京大学理学系研究科)
『 Beilinson-Drinfeld chiral algebra, geometric Langlands program and open Gromov-Witten invariants 』
都合により、とりやめになりました。
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
原下秀士 氏 (北海道大学・学振)
『 Configuration of the central streams in the moduli of abelian varieties 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
廣惠 一希 氏 (東京大学大学院数理科学研究科)
『 Hecke-Siegel's pull back formula for the Epstein zeta function with spherical 』
16:30 - 18:45 数理科学研究科棟(駒場) 117号室
Kai Köehler 氏 (Düesseldorf 大学) 16:30 - 17:30
『 Quaternionic analytic torsion and arithmetic geometry 』
Thomas Geisser 氏 (南カリフォルニア大学) 17:45 - 18:45
『 Duality via cycle complexes 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
伴 克馬 氏 (東京大学大学院数理科学研究科)
『 Differential Operators of Rankin-Cohen-Ibukiyama Type for Automorphic Forms of Several Variables 』
16:30 - 17:30 数理科学研究科棟(駒場) 117号室
谷口 隆 氏 (東京大学大学院数理科学研究科)
『 Distributions of discriminants of cubic algebras 』