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Formes modérément ramifiées de polydisques fermés et de dentelles

Abstract : 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 XL is isomorphic to a closed L-polydisc (resp. a L-lace) on which the action of Gal(L/k) is reasonable. We show that X is isomorphic to a closed k-bidisc if and only if XL is isomorphic to a closed k-bidisc. In the formalism of graduated algebra : we calculate the first pointed cohomology set of the general linear group and of the automorphisms of the plane.
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Marc Chapuis. Formes modérément ramifiées de polydisques fermés et de dentelles. Mathématiques générales [math.GM]. Université Pierre et Marie Curie - Paris VI, 2017. Français. ⟨NNT : 2017PA066293⟩. ⟨tel-01707772⟩

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