Constructibility and Reflexivity in Non-Archimedean geometry

Abstract

Abstract We introduce a notion of constructibility for étale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constructibility for schemes via the nearby cycles functor. We use the work of R. Huber to define an adic Verdier dual and investigate the extent to which we have a six-functor formalism in this context. As an application, we show that the nearby cycles functor commutes with lower shriek. Lastly, we attempt to classify those sheaves that are reflexive with respect to the adic Verdier dual.