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arXiv · 1601.00885

Parallel transport and the p-adic Simpson correspondence

Daxin Xu
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Abstract

Deninger and Werner developed an analogue for p-adic curves of the classical correspondence of Narasimhan and Seshadri between stable bundles of degree zero and unitary representations of the topological fundamental group for a complex smooth proper curve. Using parallel transport, they associated functorially to every vector bundle on a p-adic curve whose reduction is strongly semi-stable of degree 0 a p-adic representation of the fundamental group of the curve. They asked several questions: whether their functor is fully faithful; whether the cohomology of the local systems produced by this functor admits a Hodge-Tate filtration; and whether their construction is compatible with the p-adic Simpson correspondence developed by Faltings. We answer these questions in this article.

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Daxin Xu. 2016-01-05. Parallel transport and the p-adic Simpson correspondence. https://doi.org/10.1017/fms.2017.7

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