Adic space

Summary

An adic space is a geometric space, introduced by Roland Huber, whose points are continuous valuations on topological rings, see the definition. Adic spaces give one framework for non-Archimedean geometry that contains the rigid analytic spaces over a complete non-Archimedean field and also locally Noetherian formal schemes. Their points include the classical points and extra points of higher rank, which make the topology work well. Perfectoid spaces are adic spaces of a special kind.