MIT Libraries homeMIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Doctoral Theses
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Quantum geometric Langlands correspondence in positive characteristic: the GLN case

Author(s)
Travkin, Roman (Roman Mikhailovich)
Thumbnail
DownloadFull printable version (3.154Mb)
Other Contributors
Massachusetts Institute of Technology. Dept. of Mathematics.
Advisor
Roman Bezrukavnikov.
Terms of use
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
Metadata
Show full item record
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).
 
Date issued
2012
URI
http://hdl.handle.net/1721.1/73434
Department
Massachusetts Institute of Technology. Department of Mathematics
Publisher
Massachusetts Institute of Technology
Keywords
Mathematics.

Collections
  • Doctoral Theses

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries homeMIT Libraries logo

Find us on

Twitter Facebook Instagram YouTube RSS

MIT Libraries navigation

SearchHours & locationsBorrow & requestResearch supportAbout us
PrivacyPermissionsAccessibility
MIT
Massachusetts Institute of Technology
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.