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Geometric Langlands in prime characteristic

Chen, Tsao-Hsien and Zhu, Xinwen (2017) Geometric Langlands in prime characteristic. Compositio Mathematica, 153 (2). pp. 395-452. ISSN 0010-437X. doi:10.1112/S0010437X16008113.

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Let G be a semi-simple algebraic group over an algebraically closed field k, whose characteristic is positive and does not divide the order of the Weyl group of G, and let Ğ be its Langlands dual group over k. Let C be a smooth projective curve over k of genus at least two. Denote by Bun_G the moduli stack of G-bundles on C and LocSys_Ğ the moduli stack of Ğ-local systems on C. Let D_(Bun_G) be the sheaf of crystalline differential operators on Bun_G. In this paper we construct an equivalence between the bounded derived category D^b (QCoh(LocSys^0_Ğ)) of quasi-coherent sheaves on some open subset LocSys^0_Ğ ⊂ LocSys_Ğ and bounded derived category D^b (D^0_(Bun_G) -mod) of modules over some localization D^0_(Bun_G) of D_(Bun_G). This generalizes the work of Bezrukavnikov and Braverman in the GL_n case.

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Additional Information:© 2017 Foundation Compositio Mathematica. Received 21 June 2014, accepted in final form 19 January 2016, published online 16 February 2017. We thank Roman Bezrukavnikov, Roman Travkin and Zhiwei Yun for useful discussions, and Uwe Weselmann for helpful comments and suggestions. The first author would like to thank his advisor Roman Bezrukavnikov for continuous interest in this work and for much helpful advice. T.-H. Chen is partially supported by NSF under the agreement no. DMS-1128155. X. Zhu is partially supported by NSF grants DMS-1001280/1313894 and DMS-1303296 and an AMS Centennial Fellowship.
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AMS Centennial FellowshipUNSPECIFIED
Subject Keywords:Langlands duality; Hitchin fibration; D-modules in characteristic p
Issue or Number:2
Classification Code:2010 Mathematics Subject Classification 14D24, 22E57 (primary)
Record Number:CaltechAUTHORS:20140919-164520106
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Official Citation:Chen, T., & Zhu, X. (2017). Geometric Langlands in prime characteristic. Compositio Mathematica, 153(2), 395-452. doi:10.1112/S0010437X16008113
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:49882
Deposited By: George Porter
Deposited On:22 Sep 2014 19:55
Last Modified:10 Nov 2021 18:49

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