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Rigidity and a Riemann–Hilbert correspondence for p-adic local systems

Liu, Ruochuan and Zhu, Xinwen (2017) Rigidity and a Riemann–Hilbert correspondence for p-adic local systems. Inventiones Mathematicae, 207 (1). pp. 291-343. ISSN 0020-9910.

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We construct a functor from the category of p-adic étale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection on its “base change to B_(dR)”, which can be regarded as a first step towards the sought-after p-adic Riemann–Hilbert correspondence. As a consequence, we obtain the following rigidity theorem for p-adic local systems on a connected rigid analytic variety: if the stalk of such a local system at one point, regarded as a p-adic Galois representation, is de Rham in the sense of Fontaine, then the stalk at every point is de Rham. Along the way, we also establish some basic properties of the p-adic Simpson correspondence. Finally, we give an application of our results to Shimura varieties.

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Additional Information:© 2016 Springer-Verlag Berlin Heidelberg. Received: 23 March 2016; Accepted: 19 May 2016; Published online: 14 June 2016. R. Liu is partially supported by NSFC-11571017 and the Recruitment Program of Global Experts of China. X. Zhu is partially supported by NSF DMS-1303296/1535464 and a Sloan Fellowship.
Funding AgencyGrant Number
National Natural Science Foundation of ChinaNSFC-11571017
Global Experts of ChinaUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20170216-110846474
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Official Citation:Liu, R. & Zhu, X. Invent. math. (2017) 207: 291. doi:10.1007/s00222-016-0671-7
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74375
Deposited By: Tony Diaz
Deposited On:16 Feb 2017 19:49
Last Modified:03 Oct 2019 16:38

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