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On the Grothendieck--Serre conjecture concerning principal G-bundles over semi-local Dedekind domains

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arxiv 1512.00354 v1 pith:ZLQF4JG3 submitted 2015-12-01 math.AG

Ivan Panin , Anastasia Stavrova This is my paper · ORCID
classification math.AG
keywords dedekindschemesemi-localsemisimpleconcerningconjectureconnectedcontains
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Let R be a semi-local Dedekind domain and let K be the field of fractions of R. Let G be a reductive semisimple simply connected R-group scheme such that every semisimple normal R-subgroup scheme of G contains a split R-torus G_m. We prove that the kernel of the map H^1_et(R,G)-> H^1_et(K,G) induced by the inclusion of R into K, is trivial. This result partially extends a theorem of Nisnevich.

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  1. Constant case of the Grothendieck-Serre conjecture in mixed characteristic

    math.AG 2024-12 conditional novelty 8.0 of 10

    The constant case of the Grothendieck-Serre conjecture is proved for reductive group schemes over any geometrically regular local algebra over a mixed-characteristic DVR.

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