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.