In the previous work with Xinwen Zhu we construct a p-adic analogue of the classical Riemann-Hilbert correspondence. As a by-product the de Rham periods of a general Shimura variety are obtained. In a recent joint work with Hansheng Diao, Kai-Wen Lan and Xinwen Zhu, we further establish a logarithmic version of the correspondence which enables us to establish the de Rham comparison theorem with coefficients for quasi-projective varieties and compare the de Rham periods and complex periods for a general Shimura variety.

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