Rigidity method for automorphic forms over function fields

TL;DR

This paper introduces the rigidity method for constructing automorphic forms over function fields, providing explicit local systems with applications in algebraic geometry and number theory.

Contribution

It presents a novel approach using the rigidity method to explicitly construct automorphic forms and their associated local systems over function fields.

Findings

Explicit constructions of local systems as Langlands parameters

Applications to algebraic geometry

Applications to number theory

Abstract

These are lectures given at the 2022 Arizona Winter School. It gives an introduction to the rigidity method for constructing automorphic forms for semisimple groups over function fields. The rigidity method leads to explicit constructions of local systems that are Langlands parameters of automorphic forms. The examples of local systems produced in this way have applications to algebraic geometry and number theory.