Introduction to Shtukas and their moduli

TL;DR

This paper introduces Shtukas, explores their connection to geometric objects, discusses their moduli spaces, and highlights applications to automorphic forms within the context of the Langlands program.

Contribution

It provides an accessible introduction to Shtukas, their moduli spaces, and their role in automorphic forms, bridging geometric objects with number theory.

Findings

Overview of Shtukas and their properties

Relation of Shtukas to automorphic forms

Description of moduli spaces of Shtukas

Abstract

These are lectures notes of my talks at the IHES summer school on the Langlands program in 2022. We give an introduction to the notion of Shtukas, their relation with more familiar geometric objects, their moduli spaces and applications to automorphic forms.