Weights in generalizations of Serre's conjecture

Weights in generalizations of Serre's conjecture
Michael Schein, Bar-Ilan University
August 27, 2009

Abstract:  Given a prime p and a modular form, one can associate to it a two-dimensional mod p representation of the absolute Galois group of Q. Given such a mod p representation, J.-P. Serre conjectured in the 1970's when it should arise from a modular form in this way, and, if so, what the weights and levels of the associated modular forms are. We will explain these notions and discuss generalizations of the conjecture to totally real fields and to Galois representations of arbitrary dimension, as well as theorems toward these new conjectures.