Automorphy of Hecke modules from geometry

Abstract: Cohomology of locally symmetric spaces/varieties and their compactifications make fundamental bridges between Galois and automorphic representations. While these cohomology groups have natural Hecke actions and connection to function spaces, 1. if these Hecke modules are built up by automorphic representations (automorphy) and 2. which automorphic representations appear are both non-trivial questions in general. In this talk we’ll plug various interesting cohomology groups into these questions, while our main examples will be a. cohomology of automorphic local systems over locally symmetric spaces and b. automorphic vector bundles on locally symmetric varieties, whose automorphy are proved in 1995 and 2018 respectively.

number theory

Audience: researchers in the topic

Cambridge Number Theory Seminar

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