Quantum geometric Langlands correspondence in positive characteristic: the GLN case
Name
809689574-MIT.pdf
Description
Full printable version
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3.15 MB
Format
Adobe PDF
Checksum (MD5)
93ad72f4e060381dabe5b53bc74bd674
Author(s)
Travkin, Roman (Roman Mikhailovich)
Advisor(s)
Roman Bezrukavnikov.
Date Issued
2012
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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