## Geometric Langlands in prime characteristic

##### Author(s)

Chen, Tsao-Hsien
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##### Other Contributors

Massachusetts Institute of Technology. Dept. of Mathematics.

##### Advisor

Roman Bezrukavnikov.

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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##### Department

Massachusetts Institute of Technology. Dept. of Mathematics.##### Publisher

Massachusetts Institute of Technology

##### Keywords

Mathematics.