2013/09/03 by Kiran S. Kedlaya, Kedlaya, Kiran S.
Mathematics · #13A18 #14G22 #Advanced Topology and Set Theory #FOS: Mathematics #Mathematical and Theoretical Analysis #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.1309.0574
openalex publication_date 2013/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We revisit Huber's theory of continuous valuations, which give rise to the adic spectra used in his theory of adic spaces. We instead consider valuations which have been reified, i.e., whose value groups have been forced to contain the real numbers. This yields reified adic spectra which provide a framework for an analogue of Huber's theory compatible with Berkovich's construction of nonarchimedean analytic spaces. As an example, we extend the theory of perfectoid spaces to this setting.