2026-09-19T11:51:35Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/734342022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Roman Bezrukavnikov.
Travkin, Roman (Roman Mikhailovich)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2012-09-27T18:11:41Z
2012-09-27T18:11:41Z
2012
2012
http://hdl.handle.net/1721.1/73434
809689574
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
In title on title page, "N" of GLN appears as subscript of upper case letter N. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 73).
Let C be a smooth connected projective curve of genus > 1 over an algebraically closed field k of characteristic p > 0, and c [epsilon] k \ Fp. Let BunN be the stack of rank N vector bundles on C and Ldet the line bundle on BunN given by determinant of derived global sections. In this thesis, we construct an equivalence of derived categories of modules for certain localizations of the twisted crystalline differential operator algebras DBunNet and DBunN, L-1/cdet The first step of the argument is the same as that of [BB] for the non-quantum case: based on the Azumaya property of crystalline differential operators, the equivalence is constructed as a twisted version of Fourier-Mukai transform on the Hitchin fibration. However, there are some new ingredients. Along the way we introduce a generalization of p-curvature for line bundles with non-flat connections, and construct a Liouville vector field on the space of de Rham local systems on C.
by Roman Travkin.
Ph.D.
73 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Quantum geometric Langlands correspondence in positive characteristic: the GLN case
Thesis
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Publication
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<Abstract>Let C be a smooth connected projective curve of genus > 1 over an algebraically closed field k of characteristic p > 0, and c [epsilon] k \ Fp. Let BunN be the stack of rank N vector bundles on C and Ldet the line bundle on BunN given by determinant of derived global sections. In this thesis, we construct an equivalence of derived categories of modules for certain localizations of the twisted crystalline differential operator algebras DBunNet and DBunN, L-1/cdet The first step of the argument is the same as that of [BB] for the non-quantum case: based on the Azumaya property of crystalline differential operators, the equivalence is constructed as a twisted version of Fourier-Mukai transform on the Hitchin fibration. However, there are some new ingredients. Along the way we introduce a generalization of p-curvature for line bundles with non-flat connections, and construct a Liouville vector field on the space of de Rham local systems on C.</Abstract>
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