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• W2118893669 abstract "Let k be an infinite field. Let R be the semi-local ring of a finite family of closed points on a k-smooth affine irreducible variety, let K be the fraction field of R, and let G be a reductive simple simply connected R-group scheme isotropic over R. We prove that for any Noetherian k-algebra A, the map of etale cohomology sets H^1(Aotimes_k R,G)-> H^1(Aotimes_ k K,G), induced by the inclusion of R into K, has trivial kernel. This implies the Serre-Grothendieck conjecture for such groups G. The main theorem for A=k and some other results of the present paper are used significantly in arXiv:1211.2678 to prove the Serre-Grothendieck conjecture for all reductive groups over a regular semi-local ring containing an infinite field." @default.
• W2118893669 created "2016-06-24" @default.
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• W2118893669 date "2009-05-09" @default.
• W2118893669 modified "2023-09-26" @default.
• W2118893669 title "On Grothendieck--Serre's conjecture concerning principal G-bundles over reductive group schemes:I" @default.
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• W2118893669 doi "https://doi.org/10.48550/arxiv.0905.1418" @default.
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