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Quantum geometric Langlands correspondence in positive characteristic: the GLN case

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dc.contributor.advisor Roman Bezrukavnikov. en_US Travkin, Roman (Roman Mikhailovich) en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2012-09-27T18:11:41Z 2012-09-27T18:11:41Z 2012 en_US 2012 en_US
dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. en_US
dc.description In title on title page, "N" of GLN appears as subscript of upper case letter N. Cataloged from PDF version of thesis. en_US
dc.description Includes bibliographical references (p. 73). en_US
dc.description.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. en_US
dc.description.statementofresponsibility by Roman Travkin. en_US
dc.format.extent 73 p. en_US
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights 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. en_US
dc.rights.uri en_US
dc.subject Mathematics. en_US
dc.title Quantum geometric Langlands correspondence in positive characteristic: the GLN case en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 809689574 en_US

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