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Six operations for D-cap-modules on rigid analytic spaces
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We introduce all six operations for D-cap-modules on smooth rigid analytic spaces by considering the derived category of complete bornological D-cap-modules. We then focus on a full subcategory which should be thought of as consisting of complexes with coadmissible cohomology, and establish analogues of some classical results: Kashiwara's equivalence, stability of coadmissibility under extraordinary inverse image for smooth morphisms and direct image for projective morphisms, as well as the computation of relative de Rham cohomology.
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A fully faithful p-adic Riemann-Hilbert functor for coadmissible D-cap-modules
A p-adic Riemann-Hilbert correspondence is established: after base change to the overconvergent almost de Rham period sheaf, the solution functor becomes fully faithful on coadmissible D-modules.
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