2026-09-19T22:54:59Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/733592022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Roman Bezrukavnikov.
Chen, Tsao-Hsien
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2012-09-27T15:25:09Z
2012-09-27T15:25:09Z
2012
2012
http://hdl.handle.net/1721.1/73359
809543658
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2012.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 109-110).
Let C be a smooth projective curve over an algebraically closed field k of sufficiently large characteristic. Let G be a semisimple algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the moduli stack of G-bundles on C and LocSysGv the moduli stack of Gv-local systems on C. Let DBunG be the sheaf of crystalline differential operator algebra on BunG. In this thesis I construct an equivalence between the derived category D(QCoh(LocSys~v)) of quasi-coherent sheaves on some open subset LocSysov C LocSysGv and derived category D(DOunG mod) of modules over some localization DBunG of DBunG. This generalizes the work of Bezrukavnikov-Braverman in the GL, case.
by Tsao-Hsien Chen.
Ph.D.
110 p.
eng
Massachusetts Institute of Technology
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
Mathematics.
Geometric Langlands in prime characteristic
Thesis
application/pdf
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="b4040c57-10a9-4279-bc30-ebc733cf3fd4">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Language>eng</Language>
<Title>Geometric Langlands in prime characteristic</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2012</PublicationDate>
<Authors>
<Author>
<DisplayName>Chen, Tsao-Hsien</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://dspace.mit.edu/handle/1721.1/7582</License>
<Keyword>Mathematics.</Keyword>
<Abstract>Let C be a smooth projective curve over an algebraically closed field k of sufficiently large characteristic. Let G be a semisimple algebraic group over k and let GV be its Langlands dual group over k. Denote by BunG the moduli stack of G-bundles on C and LocSysGv the moduli stack of Gv-local systems on C. Let DBunG be the sheaf of crystalline differential operator algebra on BunG. In this thesis I construct an equivalence between the derived category D(QCoh(LocSys~v)) of quasi-coherent sheaves on some open subset LocSysov C LocSysGv and derived category D(DOunG mod) of modules over some localization DBunG of DBunG. This generalizes the work of Bezrukavnikov-Braverman in the GL, case.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>