A Simpson correspondence for abelian varieties in characteristic p > 0

Yun Hao

A Simpson correspondence for abelian varieties in characteristic p > 0

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arxiv 1910.12405 v1 pith:26CGLSVM submitted 2019-10-28 math.AG

Yun Hao This is my paper

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keywords abeliancharacteristicalgebraicallyapproachazumayabasebundlesclosed

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Let X/k be an abelian variety over an algebraically closed field k of characteristic p > 0. In this paper, using the Azumaya property of the sheaf of crystalline differential operators and the Morita equivalence, we show that etale locally over the Hitchin base, the moduli stack of Higgs bundles on the Frobenius twist X' is equivalent to that of local systems on X. We follow the approach of [Gro16].

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A note on Azumaya algebras and one-forms
math.AG 2026-05 unverdicted novelty 5.0 of 10

Whenever a smooth variety has a non-closed global one-form, there exists a degree one cover of its Frobenius twist where the associated Azumaya algebra does not split.

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