A six-functor formalism for quasi-coherent sheaves and stratifications on rigid-analytic varieties

TL;DR

This paper develops a six-functor formalism for quasi-coherent sheaves and stratifications on derived rigid spaces, linking analytic crystals to D-cap-modules, advancing the theoretical framework of rigid-analytic geometry.

Contribution

It introduces a new six-functor formalism for quasi-coherent sheaves and stratifications on derived rigid spaces, connecting analytic crystals with D-cap-modules.

Findings

Established a six-functor formalism for quasi-coherent sheaves

Linked analytic crystals to D-cap-modules

Developed a theory of derived rigid spaces

Abstract

We develop a theory of derived rigid spaces and quasi-coherent sheaves and analytic "stratifications" on them. Amongst other things, we obtain a six-functor formalism for these quasi-coherent sheaves and analytic stratifications. We provide evidence that the category of analytic crystals is related to the theory of D-cap-modules introduced by Ardakov--Wadsley.