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Variation de la dimension relative en géométrie analytique \(p\)-adique; Variation of relative dimension in \(p\)-adic analytic geometry. (French) Zbl 1161.14018
Author’s abstract: Let \(k\) be a complete, non-Archimedean valued field (the trivial absolute value is allowed) and let \(\varphi :X\rightarrow Y\) be a morphism between two Berkovich \(k\)-analytic spaces; we show that, for any integer \(n\), the set of points of \(X\) at which the local dimension of \(\varphi \) is at least equal to \(n\) is a Zariski-closed subset of \(X\). In order to establish it, we first prove an analytic analogue of Zariski’s Main Theorem, and we also introduce, and study, the notion of an analytic system of parameters at a point.

MSC:
14G22 Rigid analytic geometry
14A99 Foundations of algebraic geometry
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