東大数理セミナー情報 --- 代数幾何学セミナー

| 過去の記録 ～03/12 | 今後の予定 03/13～ | 談話会・セミナー ホーム | 東大数理 ホーム | 数理へのアクセス |

今後のセミナー予定

2010年04月05日(月)

16:40 - 18:10 数理科学研究科棟(駒場) 126号室

Alexandru Dimca 氏 (Université Nice-Sophia Antipolis)

『 From Lang's Conjecture to finiteness properties of Torelli groups 』

First we recall one of Lang's conjectures in diophantine geometry
on the interplay between subvarieties and translated subgroups in a
commutative algebraic group
(proved by M. Laurent in the case of affine tori in 1984).

Then we present the technique of resonance and characteristic varieties,
a powerful tool in the study of fundamental groups of algebraic varieties.


Finally, using the two ingredients above, we show that the Torelli
groups $T_g$
have some surprising finiteness properties for $g>3$.
In particular, we show that for any subgroup $N$ in $T_g$ containing
the Johnson kernel $K_g$, the complex vector space $N_{ab} \otimes C$
is finite dimensional.

All the details are available in our joint preprint with S. Papadima
arXiv:1002.0673.