The spectral gluing theorem revisited

TL;DR

This paper refines the spectral gluing theorem in the geometric Langlands conjecture, explicitly identifying the essential image of the embedding of IndCoh_N(LS_G) into a category constructed from Fourier coefficients.

Contribution

It provides a precise description of the essential image of the spectral gluing functor, strengthening previous results in the geometric Langlands program.

Findings

Explicit identification of the essential image of the spectral gluing functor.

Strengthened version of the spectral gluing theorem.

Enhanced understanding of the categorical structure in geometric Langlands.

Abstract

We strengthen the gluing theorem occurring on the spectral side of the geometric Langlands conjecture. While the latter embeds $IndCoh_N(LS_G)$ into a category glued out of 'Fourier coefficients' parametrized by standard parabolics, our refinement explicitly identifies the essential image of such embedding.