Localization and coalescence of condensed ringed spaces

Abstract

Gillam proved that the category of locally ringed spaces admits a fully faithful embedding into a certain category, which has a right adjoint that maps some simple objects to the spectra of rings. In this paper, we use condensed mathematics to define an analogous category and its coreflective full subcategories, and prove that one of their coreflections maps certain simple objects to the adic spectra of certain Huber pairs.