Reified valuations and adic spectra
© The Author(s) 2015
Received: 20 March 2015
Accepted: 19 August 2015
Published: 9 December 2015
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.