Perverse sheaves on infinite-dimensional stacks, and affine Springer theory

Alexis Bouthier, David Kazhdan, Yakov Varshavsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The goal of this work is to construct a perverse t-structure on the ∞-category of ℓ-adic LG-equivariant sheaves on the loop Lie algebra Lg and to show that the affine Grothendieck–Springer sheaf S is perverse. Moreover, S is an intermediate extension of its restriction to the locus of “compact” elements with regular semi-simple reduction. Note that classical methods do not apply in our situation because LG and Lg are infinite-dimensional ind-schemes.

Original languageAmerican English
Article number108572
JournalAdvances in Mathematics
Volume408
DOIs
StatePublished - 29 Oct 2022

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.

Keywords

  • Affine Springer theory
  • Dimension theory
  • Loop groups
  • Perverse sheaves
  • Placid infinity-stacks
  • Semi-small maps
  • t-Structures

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