A higher weight (and automorphic) generalization of the Hermite-Minkowski theorem

by Gaëtan Chenevier (CNRS, Université Paris-Sud)

Wednesday Dec 12, 2018, 10:00 AM → 11:00 AM Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

I will show that for any integer N, there are only finitely many cuspidal algebraic automorphic representations of GL_m over Q whose Artin conductor is N and whose "weights" are in the interval {0,...,23} (with m varying). Via the conjectural yoga between geometric Galois representations (or motives) and algebraic automorphic forms, this statement may be viewed as a generalization of the classical Hermite-Minkowski theorem in algebraic number theory. I will also discuss variants of these results when the base field Q is replaced by an arbitrary number field.