The adic spaces are the basic object in Huber’s approach to non-archimedean analytic geometry. They are built by gluing valuation spectra of certain class of topological rings. Unlike Berkovich analytic spectra the points correspond to valuations of arbitrary rank, not only rank one. If a Berkovich space is corresponding to a separated rigid analytic space? then it can be obtained as the largest Hausdorff quotient of the corresponding adic space.

R. Huber, Étale cohomology of rigid analytic varieties and adic spaces, Aspects of Mathematics, E30. Friedr. Vieweg & Sohn, Braunschweig, 1996. x+450 pp. MR2001c:14046

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