Local-Global Compatibility and Monodromy

GALOIS REPRESENTATIONS AND AUTOMORPHIC FORMS SEMINAR
Topic:Local-Global Compatibility and Monodromy
Speaker:Ana Caraiani
Affiliation:Harvard University
Date:Thursday, January 20
Time/Room:2:15pm - 3:15pm/S-101
Video Link:https://video.ias.edu/galois/caraiani

Given a cuspidal automorphic representation of GL(n) which is regular algebraic and conjugate self-dual, one can associate to it a Galois representation. This Galois representation is known in most cases to be compatible with local Langlands. When n is even, the compatibility is known up to semisimplification or when the representation satisfies an additional regularity condition. I will extend the compatibility to Frobenius semisimplification by identifying the monodromy operators