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