Sur les composantes connexes d'une famille d'espaces analytiques p-adiques

Abstract

Let $X=\mathcal{M}(A)$ be an affinoid space and let $f,g\in A$. We study the sets of connected components of the spaces defined by an inequality of the form $|f|\le r|g|$, with $r\ge 0$. We prove that there exists a finite partition of ${\mathbb{R}}_{+}$ into intervals where those sets are canonically in bijection and that the bounds of those intervals belong to $\sqrt{\rho (A)}$.

18 pages, in French

Cited by in corpus (1)

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