A note on p-adic Simpson correspondence

2020/12/03 by Yang, Jinbang, Zuo, Kang
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2012.02058

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 \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 étale fundamental group.

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