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Title:Tamely ramified geometric Langlands correspondence in positive characteristic
Author(s):Shen, Shiyu
Director of Research:Nevins, Thomas
Doctoral Committee Chair(s):Haboush, William
Doctoral Committee Member(s):McGerty, Kevin; Dodd, Christopher
Department / Program:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):Hitchin systems, geometric Langlands correspondence
Abstract: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.
Issue Date:2019-07-09
Rights Information:2019 by Shiyu Shen. All rights reserved.
Date Available in IDEALS:2019-11-26
Date Deposited:2019-08

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