Equivariant localization and base change functoriality

Abstract: Lafforgue and Genestier-Lafforgue have constructed the global and (semisimplified) local Langlands correspondences for arbitrary reductive groups over function fields. I will explain some recently established properties of these correspondences regarding base change functoriality: existence of transfers for mod $p$ automorphic forms through $p$-cyclic base change in the global correspondence, and Tate cohomology realizes $p$-cyclic base change in the mod $p$ local correspondence. In particular, the local statement verifies a conjecture of Treumann-Venkatesh.

number theory

Audience: researchers in the topic

( slides )

UCLA Number Theory Seminar