A Simpson correspondence for abelian varieties in characteristic p > 0
Algebraic Geometry
2019-10-29 v1
Abstract
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].
Keywords
Cite
@article{arxiv.1910.12405,
title = {A Simpson correspondence for abelian varieties in characteristic p > 0},
author = {Yun Hao},
journal= {arXiv preprint arXiv:1910.12405},
year = {2019}
}