A resolution of singularities for Drinfeld's compactification by stable maps

TL;DR

This paper introduces a resolution of singularities for Drinfeld's compactification using stable maps, revealing new insights into the intersection cohomology and its local properties in automorphic sheaves.

Contribution

It provides a novel resolution of singularities for Drinfeld's compactification via stable maps from nodal curves into twisted flag varieties.

Findings

Proves the twisted intersection cohomology sheaf is universally locally acyclic over the moduli stack of G-bundles.

Establishes a connection between singularities and representation-theoretic information.

Enhances understanding of automorphic sheaves and their geometric properties.

Abstract

Drinfeld's relative compactification plays a basic role in the theory of automorphic sheaves, and its singularities encode representation-theoretic information in the form of intersection cohomology. We introduce a resolution of singularities consisting of stable maps from nodal deformations of the curve into twisted flag varieties. As an application, we prove that the twisted intersection cohomology sheaf on Drinfeld's compactification is universally locally acyclic over the moduli stack of $G$-bundles at points sufficiently antidominant relative to their defect.