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.
Keywords
Cite
@article{arxiv.2110.09398,
title = {Six operations for D-cap-modules on rigid analytic spaces},
author = {Andreas Bode},
journal= {arXiv preprint arXiv:2110.09398},
year = {2025}
}
Comments
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