# Galois Representations for Regular Algebraic Cuspidal Automorphic Forms

 Joint IAS/PU Number Theory Seminar Topic: Galois Representations for Regular Algebraic Cuspidal Automorphic Forms Speaker: Richard Taylor Affiliation: Professor, School of Mathematics, IAS Date: Thursday, November 15 Time/Room: 4:30pm - 5:30pm/S-101 Video Link: https://video.ias.edu/jointiaspu/taylor

To any essentially self-dual, regular algebraic (ie cohomological) automorphic representation of GL(n) over a CM field one knows how to associate a compatible system of l-adic representations. These l-adic representations occur (perhaps slightly twisted) in the cohomology of a Shimura variety. Recently Harris, Lan, Thorne and myself have constructed l-adic representations without the essentially self-dual ‘hypothesis'. In this case the l-adic representations do not occur in the cohomology of any Shimura variety. Rather we construct them using a congruence argument. In this talk I will describe this theorem and sketch the proof.