Six operations for D-cap-modules on rigid analytic spaces

Abstract

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.

Corrected and expanded version. Key changes are an extension of almost all results to arbitrary complete base fields and the use of Ind-Banach spaces, as complete bornological spaces do not form an elementary category