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  "body": "\n## Summary\n\nAn adic space is a geometric space, introduced by Roland Huber, whose points are continuous valuations on topological rings, see the [[definition|5AXZG4PXTE]].\nAdic spaces give one framework for non-Archimedean geometry that contains the [[rigid analytic spaces|YAH6MZVG7K]] over a complete non-Archimedean field and also locally Noetherian formal schemes.\nTheir points include the classical points and extra points of higher rank, which make the topology work well.\n[[Perfectoid spaces|Q9Y4CJE1X5]] are adic spaces of a special kind.\n\n## Explanations\n\n### L1 human\n\nIn ordinary geometry, a point of a space is a way to evaluate functions.\nIn an adic space, a point is a way to measure the size of functions, given by a valuation.\nThe model case is the $p$-adic closed unit disc, built from power series with $p$-adic coefficients tending to $0$, which converge on the disc.\nBesides the usual points, it has points that measure functions by their largest size on a smaller disc, and some infinitesimal refinements of these.\nWith these extra points, coverings behave as they should, so functions defined piece by piece can be glued.\n",
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