Toute forme mod 'er 'ement ramifi 'ee d'un polydisque ouvert est\n triviale

2011/06/01 by Antoine Ducros, Ducros, Antoine · 1 citation
Mathematics · #14G20 #14G22 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.1106.0135

openalex publication_date 2011/06/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Let k be a complete, non-Archimedean field and let X be a k-analytic space ;\nassume that there exists a tamely ramified finite extension L/k such that X_L\nis isomorphic to an open polydisc over L ; we prove that X is itself isomorphic\nto an open polydisc over k. The proof consists in using the em graded\nreduction (a notion which is due to Temkin) of the algebra of functions on X,\ntogether with some graded counterparts of classical commutative algebra\nresults: Nakayama's lemma, going-up theorem, basic notions about 'etale\nalgebras, etc.\n

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