Fourier coefficients and a filtration on Shv(Bun_G)

TL;DR

The paper introduces a new filtration on the sheaf category over the moduli of G-torsors, linking it to the spectral side of the geometric Langlands conjecture and proposing compatibility with parabolic induction.

Contribution

It defines a DG-filtration on Shv(Bun_G) stable under Hecke actions and conjectures its relation to the spectral filtration and parabolic induction in geometric Langlands.

Findings

Proposes a DG-filtration on sheaves over Bun_G

Formulates a conjecture relating the filtration to spectral side

Suggests compatibility with parabolic induction

Abstract

We define a filtration by DG-subcategories on the DG-category Shv(Bun_G) of sheaves on the moduli of G-torsors on a curve, which is stable under the action of Hecke functors. We formulate a conjecture relating this filtration with another filtration on the spectral side of the categorical geometric Langlands conjecture. We also formulate a conjectural compatibility with the parabolic induction.