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Abstract

In this article, we construct the abelian category of coadmissible $p$-adic $\mathcal{D}^{\infty}$-modules on a smooth rigid analytic variety over a complete discrete valued field. We also consider equivariant $\mathcal{D}^{\infty}$-modules and prove a $p$-adic analogue of the Beilinson-Bernstein localization theorem for admissible locally analytic representations.

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