Derived non-archimedean analytic spaces

摘要

We propose a derived version of non-archimedean analytic geometry. Intuitively, a derived non-archimedean analytic space consists of an ordinary non-archimedean analytic space equipped with a sheaf of derived rings. Such a naive definition turns out to be insufficient. In this paper, we resort to the theory of pregeometries and structured topoi introduced by Jacob Lurie. We prove the following three fundamental properties of derived non-archimedean analytic spaces:The category of ordinary non-archimedean analytic spaces embeds fully faithfully into the -category of derived non-archimedean analytic spaces.