The horizontal sections functor using the overconvergent de Rham period structure sheaf agrees with Scholze's using OBdR on smooth rigid-analytic varieties, identifying it with the de Rham functor for D-cap-modules.
A fully faithful p-adic Riemann-Hilbert functor for coadmissible D-cap-modules
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abstract
This article establishes a Riemann-Hilbert correspondence in rigid-analytic geometry. We construct an explicit solution functor and prove that it is fully faithful on Ardakov-Wadsley's coadmissible D-cap-modules. For vector bundles with flat connection, our functor is canonically identified with Scholze's horizontal sections functor.
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2026 1verdicts
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The p-adic Cauchy Theorem and Overconvergent Period Sheaves
The horizontal sections functor using the overconvergent de Rham period structure sheaf agrees with Scholze's using OBdR on smooth rigid-analytic varieties, identifying it with the de Rham functor for D-cap-modules.