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.