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

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 $\{x\in X,|f(x)|\ge \epsilon \}$ behave with regards to $\epsilon$. We also obtain a result concerning privileged neighbourhoods and adapt a theorem from complex analytic geometry about Noetherianity for germs of analytic functions.

Slight improvements of theorems 1 and 2. Final version. 46 pages

Cited by in corpus (2)

• Analytic functions on tubes of non-Archimedean analytic spaces
• Cohomology of algebraic varieties over non-archimedean fields