Constructibility and Reflexivity in non-Archimedean geometry

TL;DR

This paper develops a framework for constructibility and reflexivity of étale sheaves on adic spaces in non-Archimedean geometry, extending classical concepts and exploring duality and functorial formalism.

Contribution

It introduces a new notion of constructibility for étale sheaves on adic spaces and investigates the properties of the adic Verdier dual, advancing the understanding of sheaf theory in non-Archimedean geometry.

Findings

Defined constructibility for étale sheaves on adic spaces.

Established properties of the adic Verdier dual.

Explored classification of reflexive sheaves.

Abstract

We introduce a notion of constructibility for \'etale 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 6-functor formalism in this context. Lastly, we attempt to classify those sheaves which are reflexive with respect to the adic Verdier dual.