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

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.

79 pages, v2: Substantially revised. Added section on homotopical algebra in quasi-abelian categories