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arXiv · 1707.01767

Proof of Grothendieck--Serre conjecture on principal bundles over regular local rings containing a finite field

Ivan Panin
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Abstract

Let R be a regular local ring, containing a finite field. Let G be a reductive group scheme over R. We prove that a principal G-bundle over R is trivial, if it is trivial over the fraction field of R. If the regular local ring R contains an infinite field this result is proved in [FP]. Thus the conjecture is true for regular local rings containing a field.

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Ivan Panin. 2017-07-05. Proof of Grothendieck--Serre conjecture on principal bundles over regular local rings containing a finite field. https://arxiv.org/abs/1707.01767

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