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Geometric Langlands in prime characteristic

Author(s)
Chen, Tsao-Hsien
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Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Roman Bezrukavnikov.
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M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582
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Abstract
Let C be a smooth projective curve over an algebraically closed field k of sufficiently large characteristic. Let G be a semisimple algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the moduli stack of G-bundles on C and LocSysGv the moduli stack of Gv-local systems on C. Let DBunG be the sheaf of crystalline differential operator algebra on BunG. In this thesis I construct an equivalence between the derived category D(QCoh(LocSys~v)) of quasi-coherent sheaves on some open subset LocSysov C LocSysGv and derived category D(DOunG mod) of modules over some localization DBunG of DBunG. This generalizes the work of Bezrukavnikov-Braverman in the GL, case.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
 
Cataloged from PDF version of thesis.
 
Includes bibliographical references (p. 109-110).
 
Date issued
2012
URI
http://hdl.handle.net/1721.1/73359
Department
Massachusetts Institute of Technology. Dept. of Mathematics.
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

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  • Mathematics - Ph.D. / Sc.D.
  • Mathematics - Ph.D. / Sc.D.

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