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過去の記録 ～06/25｜次回の予定｜今後の予定 06/26～
| 開催情報 | 金曜日 13:30～15:00 数理科学研究科棟(駒場) 118号室 |
|---|---|
| 担当者 | 權業 善範、河上 龍郎 、榎園 誠 |
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
Alexandru Dimca 氏 (Université Nice-Sophia Antipolis)
From Lang's Conjecture to finiteness properties of Torelli groups
[ 講演概要 ]
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 Tg
have some surprising finiteness properties for g>3.
In particular, we show that for any subgroup N in Tg containing
the Johnson kernel Kg, the complex vector space NabotimesC
is finite dimensional.
All the details are available in our joint preprint with S. Papadima
arXiv:1002.0673.
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 Tg
have some surprising finiteness properties for g>3.
In particular, we show that for any subgroup N in Tg containing
the Johnson kernel Kg, the complex vector space NabotimesC
is finite dimensional.
All the details are available in our joint preprint with S. Papadima
arXiv:1002.0673.
