Hitchin type moduli stacks in automorphic representation theory

TL;DR

This paper surveys how Hitchin moduli stacks are used in automorphic representation theory over function fields, aiding in the comparison of trace formulae and applications to fundamental lemmas and the Gross-Zagier formula.

Contribution

It provides an overview of the applications of Hitchin moduli stacks in key problems of automorphic representation theory, highlighting their geometric role.

Findings

Hitchin stacks facilitate comparison of trace formulae.

Applications to fundamental lemmas are elucidated.

Connections to the higher Gross-Zagier formula are discussed.

Abstract

In the study of automorphic representations over a function field, Hitchin moduli stack and its variants naturally appear and their geometry helps the comparison of trace formulae. We give a survey on applications of this observation to a relative fundamental lemma, the arithmetic fundamental lemma and to the higher Gross-Zagier formula.