Moduli of flat connections in positive characteristic

Details Moduli of flat connections in positive characteristic Moduli of flat connections in positive characteristic

2012-01-03

arxiv.org/abs/1201.0741v1

Mathematics

Algebraic Geometry

34 pages, comments appreciated

Scientific paper

Exploiting the description of rings of differential operators as Azumaya algebras on cotangent bundles, we show that the moduli stack of flat connections on a curve defined over an algebraically closed field of positive characteristic is \'etale locally equivalent to a moduli stack of Higgs bundles over the Hitchin base. We then study the interplay with stability and generalize a result of Laszlo-Pauly, concerning properness of the Hitchin map. Using Arinkin's autoduality of compactified Jacobians we extend the main result of Bezrukavnikov-Braverman, the Langlands correspondence for D-modules in positive characteristic for smooth spectral curves, to the locus of integral spectral curves.

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