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On the Grothendieck-Serre conjecture on principal bundles in mixed characteristic

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arxiv 1501.04224 v3 pith:7ZMRQSUA submitted 2015-01-17 math.AG math.AC

Roman Fedorov This is my paper · ORCID
classification math.AGmath.AC
keywords conjecturefieldlocalprincipalregulartrivialwhenbundles
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Let R be a regular local ring. Let G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle over R is trivial if it is trivial over the quotient field of R. The conjecture is known when R contains a field. We prove the conjecture for a large class of regular local rings not containing fields in the case when G is split.

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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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