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Published January 2019 | Submitted
Journal Article Open

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

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.

Additional Information

© 2018 University Press, Inc. Received by editor(s): April 11, 2017; Received by editor(s) in revised form: May 28, 2018; Published electronically: October 11, 2018. I thank Dennis Gaitsgory for suggesting that I use stable maps to prove Theorem 4.2.1 and for patiently answering many questions. I also thank Sergey Lysenko for the careful reading and for comments which substantially improved the paper.

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Created:
August 19, 2023
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October 19, 2023