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arXiv · 1512.00354

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

Ivan Panin·Anastasia Stavrova
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Abstract

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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Ivan Panin, Anastasia Stavrova. 2015-12-01. On the Grothendieck--Serre conjecture concerning principal G-bundles over semi-local Dedekind domains. https://arxiv.org/abs/1512.00354

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