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Jean-Claude Douai
Sur la 2-cohomologie non abélienne des modèles réguliers des anneaux locaux henséliens
Journal de théorie des nombres de Bordeaux, 21 no. 1 (2009), p. 119-129, doi: 10.5802/jtnb.661
Article PDF | Reviews MR 2537707 | Zbl 1181.14016 | 1 citation in Cedram

Résumé - Abstract

Let $A$ be a Notherian, local, Henselien, excellent domain with algbraically closed residue field of caracteristic 0 or finite $k$, $K=Frac(A)$, $X \rightarrow Spec\ A$ a proper morphism with special fiber $X_0\rightarrow Spec \ k$ of dimension at most one. Here we complete the results of [1] showing that if $X$ is regular and if $L$ is a $X_{et}$-lien that is locally representable by a simply connected semi-simple group, then all classes of $H^2(X_{et},L)$ are neutral. Taking for $X$ a regular model of $A$, we show that all classes of $H^2(K,L)$ are neutral if $\dim (A)=2$ and if $k$ is algebraically closed of caracteristic 0. We find again some results of [2].

Bibliography

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