SMS scnews item created by Jonathan Hillman at Mon 8 Mar 2010 0852
Type: Seminar
Distribution: World
Expiry: 12 Mar 2010
Calendar1: 12 Mar 2010 1400-1500
CalLoc1: Carslaw 175
Auth: jonh@asti.maths.usyd.edu.au

# Joint Colloquium: Dimca -- From Lang’s conjecture to Torelli groups

Alex Dimca is now at the University of Nice.
(Many would remember him as a colleague at Sydney in the early 1990s!)

From Lang’s Conjecture to finiteness properties of Torelli groups

Abstract:

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.


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