Quantum geometric Langlands correspondence in positive characteristic: the GLN case
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2012
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/73434 |
| _version_ | 1826207679155011584 |
|---|---|
| author | Travkin, Roman (Roman Mikhailovich) |
| author2 | Roman Bezrukavnikov. |
| author_facet | Roman Bezrukavnikov. Travkin, Roman (Roman Mikhailovich) |
| author_sort | Travkin, Roman (Roman Mikhailovich) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012. |
| first_indexed | 2024-09-23T13:53:16Z |
| format | Thesis |
| id | mit-1721.1/73434 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:53:16Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/734342019-04-12T09:20:46Z Quantum geometric Langlands correspondence in positive characteristic: the GLN case Travkin, Roman (Roman Mikhailovich) Roman Bezrukavnikov. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2012-09-27T18:11:41Z 2012-09-27T18:11:41Z 2012 2012 Thesis http://hdl.handle.net/1721.1/73434 809689574 eng 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 73 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Travkin, Roman (Roman Mikhailovich) Quantum geometric Langlands correspondence in positive characteristic: the GLN case |
| title | Quantum geometric Langlands correspondence in positive characteristic: the GLN case |
| title_full | Quantum geometric Langlands correspondence in positive characteristic: the GLN case |
| title_fullStr | Quantum geometric Langlands correspondence in positive characteristic: the GLN case |
| title_full_unstemmed | Quantum geometric Langlands correspondence in positive characteristic: the GLN case |
| title_short | Quantum geometric Langlands correspondence in positive characteristic: the GLN case |
| title_sort | quantum geometric langlands correspondence in positive characteristic the gln case |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/73434 |
| work_keys_str_mv | AT travkinromanromanmikhailovich quantumgeometriclanglandscorrespondenceinpositivecharacteristictheglncase |