A toy model for the Drinfeld–Lafforgue shtuka construction

D. Gaitsgory*, D. Kazhdan, N. Rozenblyum, Y. Varshavsky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

The goal of this paper is to provide a categorical framework that leads to the definition of shtukas à la Drinfeld and of excursion operators à la V. Lafforgue. We take as the point of departure the Hecke action of Rep(Gˇ) on the category Shv(BunG) of sheaves on BunG, and also the endofunctor of the latter category, given by the action of the geometric Frobenius. The shtuka construction will be obtained by applying (various versions of) categorical trace.

Original languageAmerican English
Pages (from-to)39-189
Number of pages151
JournalIndagationes Mathematicae
Volume33
Issue number1
DOIs
StatePublished - Jan 2022

Bibliographical note

Publisher Copyright:
© 2021 Royal Dutch Mathematical Society (KWG)

Keywords

  • Geometric Langlands
  • Shtuka
  • Trace

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