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

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