Abstract: In this talk we will prove that some abelian surfaces are modular, in the sense that there is a paramodular form whose L-series matches that of the abelian surface. During the talk we will recall the relation between automorphic representations and algebraic varieties (with special emphasis in the case of abelian surfaces), and will describe in detail the Faltings-Serre method (and its relation with deformation theory). The talk will be self contained, and only some knowledge on Galois theory will be assumed.
ICTP - Strada Costiera, 11
I - 34151 Trieste Italy (+39) 040 2240 111 firstname.lastname@example.org