Moduli of flat connections in positive characteristic
Moduli of flat connections in positive characteristic
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DOI：
10.4310/mrl.2016.v23.n4.a3
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发表时间：
2012-01
期刊：
影响因子：
--
通讯作者：
M. Groechenig
中科院分区：
文献类型：
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作者：
M. Groechenig
利用微分算子环作为余切丛上的Azumaya代数的刻划，证明了定义在具有正特征的代数闭域上的曲线上的平坦连通的模叠(允许获得orbilold点)局部等价于Hitchin基上的Higgs丛的模叠。然后我们研究了稳定性的相互作用，推广了Laszlo-Paly关于Hitchin映射适定性的一个结果。利用紧Jacobian的Arinkin自对偶性，我们将Bezrukavnikov-Braverman的主要结果推广到积分谱曲线的轨迹上。
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 (allowed to acquire orbifold points) 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.