Geometric Langlands in prime characteristic

Tsao Hsien Chen, Xinwen Zhu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let be a semi-simple algebraic group over an algebraically closed field , whose characteristic is positive and does not divide the order of the Weyl group of , and let be its Langlands dual group over . Let be a smooth projective curve over of genus at least two. Denote by the moduli stack of -bundles on and the moduli stack of -local systems on . Let be the sheaf of crystalline differential operators on . In this paper we construct an equivalence between the bounded derived category of quasi-coherent sheaves on some open subset and bounded derived category of modules over some localization of . This generalizes the work of Bezrukavnikov and Braverman in the case.

Original languageEnglish (US)
Pages (from-to)395-452
Number of pages58
JournalCompositio Mathematica
Volume153
Issue number2
DOIs
StatePublished - Feb 1 2017
Externally publishedYes

Keywords

  • D-modules in characteristic p
  • Hitchin fibration
  • Langlands duality

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