Tamely ramified geometric Langlands correspondence in positive characteristic

We prove a version of the tamely ramified geometric Langlands correspondence in positive characteristic for GLn(k), where k is an algebraically closed field of characteristic p > n. Let X be a smooth projective curve over k with marked points, and fix a parabolic subgroup of GLn(k) at each marked point. We denote by Bun(n,P) the moduli stack of (quasi-)parabolic vector bundles on X, and by Loc(n, P) the moduli stack of parabolic flat connections such that the residue is nilpotent with respect to the parabolic reduction at each marked point. We construct an equivalence between the bounded derived category D^b(QCoh(Loc^0(n,P))) of quasi-coherent sheaves on an open substack Loc^0(n, P) of Loc(n,P), and the bounded derived category D^b(D^0Bun(n,P)-mod) of D^0Bun(n,P)-modules, where D^0Bun(n,P) is a localization of DBun(n,P) the sheaf of crystalline differential operators on Bun(n,P). Thus we extend the work of Bezrukavnikov-Braverman [8] to the tamely ramified case. We also prove a correspondence between flat connections on X with regular singularities and meromorphic Higgs bundles on the Frobenius twist X(1) of X with first order poles.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2019

Author dc:creator

• Shen, Shiyu

Contributors dc:contributor

• Nevins, Thomas
• Haboush, William
• McGerty, Kevin
• Dodd, Christopher

• Hitchin systems, geometric Langlands correspondence

Statement dc:rights

• 2019 by Shiyu Shen. All rights reserved.

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/105797

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/105797