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Berkovich \(p\)-adic analytic spaces. (Espaces analytiques \(p\)-adiques au sens de Berkovich.) (French. English summary) Zbl 1197.14020
Séminaire Bourbaki. Volume 2005/2006. Exposés Nos. 952–966. Paris: Société Mathématique de France (ISBN 978-2-85629-230-3/pbk). Astérisque 311, 137-176, Exp. No. 958 (2007).
Summary: Fifteen years ago, Berkovich suggested a new viewpoint on analytic geometry over a non-archimedean complete field; the main difference between this viewpoint and the preceeding ones is that Berkovich’s spaces are locally compact and locally arcwise connected. This approach has been very fruitful; for example it had applications to vanishing cycles, or to some \(p\)-adic analogous of classical complex theories: potential, dessins d’enfants, integration along a path, dynamical systems….
For the entire collection see [Zbl 1115.00012].

MSC:
14G22 Rigid analytic geometry
14G20 Local ground fields in algebraic geometry
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