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

• 成果类型: Article
• 署名作者: Liu, Ruochuan; Zhu, Xinwen
• 署名单位: Peking University; California Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0671-7
• 发表日期: 2017
• 页码: 291-343
• 关键词: hodge theory; families; REPRESENTATIONS

摘要

We construct a functor from the category of p-adic ,tale 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 , 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.