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arXiv · 1501.04224

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

Roman Fedorov
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Abstract

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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Roman Fedorov. 2015-01-17. On the Grothendieck-Serre conjecture on principal bundles in mixed characteristic. https://doi.org/10.1090/tran%2F8490

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