Faisceaux equivariants sur $\mathbb{P}^1$ et faisceaux automorphes

TL;DR

This paper introduces a functor linking equivariant sheaves on the projective line to automorphic sheaves on modular curves, inspired by prior work, expanding the understanding of their relationship.

Contribution

It defines and studies a new functor that connects equivariant sheaves on  to automorphic sheaves on modular curves, providing a novel perspective in the field.

Findings

Established a functor from equivariant sheaves on  to automorphic sheaves.

Extended the framework of sheaf theory in the context of modular curves.

Provided insights into the structure of automorphic sheaves via equivariant sheaves.

Abstract

Inspired by [Pan21], we define and study a functor which associates to equivariant sheaves on $\mathbb{P}^1$ automorphic sheaves on modular curves.