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arXiv · 2012.02058

A note on p-adic Simpson correspondence

Jinbang Yang·Kang Zuo
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Abstract

Given a proper smooth $p$-adic variety, we show a comparison theorem for the $p$-adic Simpson correspondence constructed by Faltings and Riemann-Hilbert correspondence constructed by Scholze. As an application we formulate a sufficient condition for $\overline{\mathbb Q}_p$-local system being de Rham. We study a $p$-adic analogue of Simpson's $\mathbb C^*$-action on the set of isomorphism classes of Higgs bundles and the corresponding Galois action on the set of isomorphism classes of generalized representations of the \'etale fundamental group.

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Jinbang Yang, Kang Zuo. 2020-12-03. A note on p-adic Simpson correspondence. https://arxiv.org/abs/2012.02058

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