Holonomic D-cap-modules on rigid analytic spaces

TL;DR

This paper extends the theory of holonomic D-modules to rigid analytic spaces, establishing stability under key operations and developing a six-functor formalism analogous to classical settings.

Contribution

It introduces a new definition of holonomic D-cap-modules on rigid analytic spaces and proves their stability under multiple fundamental operations, advancing the theory in non-Archimedean geometry.

Findings

Stability under inverse image functors

Stability under duality and direct images for projective morphisms

Development of a six-functor formalism for holonomic D-modules

Abstract

We adapt Caro's notion of overholonomicity to give a definition of holonomic D-cap-modules on rigid analytic spaces. We prove stability under five of the six operations (both inverse image functors, duality, and both direct image functors for projective morphisms), as well as base change results. Up to the open problem of stability under tensor products, we obtain an analogue of the usual six-functor formalism for holonomic D-modules.