p-adic局部系统的刚性和Riemann-Hilbert对应
Rigidity and a Riemann-Hilbert correspondence for p-adic local systems
摘要：
我们构造了一个函子，从p-adic域上光滑刚性解析簇X上的p-adic根局部系范畴到在其“B_dR的基变换”上具有可积联络的向量丛范畴，这可以被看作是向p-adic Riemann-Hilbert对应迈出的第一步.由此，我们得到了连通刚性解析簇上p-adic局部系统的刚性定理：如果这样一个局部系统在一点的茎（被认为是p-adic伽罗瓦表示）是Fontaine意义下的de Rham，则在每一点的茎都是de Rham.在此过程中，我们还建立了p-adic Simpson对应的一些基本性质。最后，我们给出了我们的结果的应用Shimura品种。
英文摘要：
We construct a functor from the category of p-adic etale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection over 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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