The six functors for Zariski-constructible sheaves in rigid geometry

We prove a generic smoothness result in rigid analytic geometry over characteristic zero non-archimedean field. The proof relies on novel notion of points which are well adapted to ‘spreading out’ arguments, analogy with the use scheme theory. As an application, we develop six-functor formalism for Zariski-constructible étale sheaves spaces. Among other things, this implies that spaces support well-behaved theory perverse sheaves.