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

2015/12/01 by Panin, Ivan, Stavrova, Anastasia · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.00354

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 H¹_et(R,G)-> H¹_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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