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Un résultat de connexité pour les variétés analytiques p-adiques. Privilège et noethérianité

Jérôme Poineau
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Abstract

Let $k$ be a non-Archimedean field, $X$ a $k$-affinoid space and $f$ an analytic function over $X$. We precisely describe how the geometric connected components of the spaces $\{x \in X, |f(x)| \ge \varepsilon\}$ behave with regards to $\varepsilon$. We also obtain a result concerning privileged neighbourhoods and adapt a theorem from complex analytic geometry about Noetherianity for germs of analytic functions.

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Jérôme Poineau. 2008-09-16. Un résultat de connexité pour les variétés analytiques p-adiques. Privilège et noethérianité. https://doi.org/10.1112/s0010437x07003016

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