Automorphic gluing functor in Betti Geometric Langlands

TL;DR

This paper develops a gluing functor in Betti Geometric Langlands, connecting automorphic categories across degenerations of curves, and models affine Hecke operators via bubbling projective lines.

Contribution

It introduces a new gluing functor for automorphic categories in Betti Geometric Langlands, relating categories of nodal and smooth curves through degeneration techniques.

Findings

Construction of a gluing functor for automorphic categories.

Realization of affine Hecke operators via bubbling projective lines.

Establishment of a connection between automorphic categories of nodal and smooth curves.

Abstract

We study automorphic categories of nilpotent sheaves under degenerations of smooth curves to nodal Deligne-Mumford curves. Our constructions realize affine Hecke operators as the result of bubbling projective lines from marked points. We use this to construct a "gluing functor" from the automorphic category of a nodal Deligne-Mumford curve to the automorphic category of a smoothing.