Irreducibility of Galois representations

Seminar
Speaker
Ariel Weiss (University of Sheffield)
Date
02/01/2019 - 11:30 - 10:30Add to Calendar 2019-01-02 10:30:00 2019-01-02 11:30:00 Irreducibility of Galois representations According to the Langlands philosophy, there should be a close relationship between automorphic representations and Galois representations. When are these Galois representations irreducible? In the 1970s, Ribet proved that the p-adic Galois representation attached to a modular form f is irreducible if and only if f is cuspidal. More generally, it is conjectured that the p-adic Galois representation associated to any cuspidal automorphic representation of GL(n) is irreducible.  The goal of this talk is to provide an overview of this conjecture, focusing on the special case of Galois representations attached to low weight, genus 2 Siegel modular forms. These two-dimensional analogues of weight 1 modular forms are, conjecturally, the automorphic objects that correspond to abelian surfaces. Third floor seminar room (room 201, building 216) אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room (room 201, building 216)
Abstract

According to the Langlands philosophy, there should be a close relationship between automorphic representations and Galois representations. When are these Galois representations irreducible?

In the 1970s, Ribet proved that the p-adic Galois representation attached to a modular form f is irreducible if and only if f is cuspidal. More generally, it is conjectured that the p-adic Galois representation associated to any cuspidal automorphic representation of GL(n) is irreducible. 

The goal of this talk is to provide an overview of this conjecture, focusing on the special case of Galois representations attached to low weight, genus 2 Siegel modular forms. These two-dimensional analogues of weight 1 modular forms are, conjecturally, the automorphic objects that correspond to abelian surfaces.

Last Updated Date : 21/12/2018