Vector bundles and local systems on non-Archimedean analytic spaces

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This project aims a deeper understanding of p-adic versions of the classical correspondences of Narasimhan-Seshadri and Simpson. Previous work of the PI together with Christopher Deninger introduces the category of vector bundles with numerically flat reduction on a proper, smooth p-adic variety to which a continuous functor of p-adic parallel transport can be associated. Würthen has shown how to reinterpret and generalize this construction on proper rigid spaces with the help of Scholze's pro-etale site. The goal of the proposed project is threefold: We want to generalize this point of view to a p-adic Narasimhan-Seshadri result for parabolic bundles, we plan to make use of Scholze's theory of diamonds to study bundles with numerically flat reduction after proper pullback, and finally we plan to attack the case of non-vanishing Higgs field.