A proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing infinite fields

摘要

Let (R) be a regular local ring containing an infinite field. Let (mathbf{G} ) be a reductive group scheme over (R). We prove that a principal (mathbf{G} )-bundle over (R) is trivial if it is trivial over the fraction field of (R). In other words, if (K) is the fraction field of (R), then the map of non-abelian cohomology pointed sets $$H^{1}_{acute{mathrm{e}}mathrm{t}}(R,mathbf{G})to H^{1}_{acute{mathrm{e}}mathrm{t}}(K, mathbf{G}) $$ induced by the inclusion of (R) into (K) has a trivial kernel. Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (38) References[Che] V. 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MathSciNet About this Article Title A proof of the Grothendieck–Serre conjecture on principal bundles over regular local rings containing infinite fields Journal Publications mathématiques de l'IHÉS Volume 122, Issue 1 , pp 169-193 Cover Date2015-11 DOI 10.1007/s10240-015-0075-z Print ISSN 0073-8301 Online ISSN 1618-1913 Publisher Springer Berlin Heidelberg Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Mathematics, general Algebra Analysis Geometry Number Theory Authors Roman Fedorov (1) Ivan Panin (2) Author Affiliations 1. Mathematics Department, Kansas State University, 138 Cardwell Hall, Manhattan, KS, 66506, USA 2. Steklov Institute of Mathematics at St.-Petersburg, Fontanka 27, St.-Petersburg, 191023, Russia Continue reading... To view the rest of this content please follow the download PDF link above.