Local-Global Compatibility and Monodromy

Local-Global Compatibility and Monodromy - Ana Caraiani

Ana Caraiani
Harvard University
January 20, 2011

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.