Formes modérément ramifiées de polydisques fermés et de dentelles

Chapuis, Marc

Annales de l'Institut Fourier, Tome 71 (2021) no. 1, pp. 287-316.

Soient $k$ un corps ultramétrique complet, $L$ une extension galoisienne finie modérément ramifiée de $k$ et $X$ un espace $k$-analytique. Nous montrons que $X$ est isomorphe à un $k$-polydisque fermé (resp. une $k$-dentelle) si et seulement si $X_L$ est isomorphe à un $L$-polydisque fermé (resp. une $L$-dentelle) sur lequel l’action de $\mathrm{Gal}(L/k)$ est raisonnable.

Let $k$ be a complete non-Archimedean field, $L$ a finite tamely ramified galoisian extension of $k$ and $X$ a $k$-analytic space. We show that $X$ is isomorphic to a closed $k$-polydisc (resp. a $k$-lace) if and only if $X_L$ is isomorphic to a closed $L$-polydisc (resp. a $L$-lace) on which the action of $\mathrm{Gal}(L/k)$ is reasonable.

Classification : 14G22, 13B02, 16W70
Mot clés : espaces de Berkovich, ramification modérée, polydisque, couronne
Keywords: Berkovich spaces, tame ramification, polydisc, annuli

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