A PROOF OF THE GROTHENDIECK-SERRE CONJECTURE ON PRINCIPAL BUNDLES OVER REGULAR LOCAL RINGS CONTAINING INFINITE FIELDS

被引：41

作者：

Fedorov, Roman ^{[1
]}

Panin, Ivan ^{[2
]}

机构：

[1] Kansas State Univ, Dept Math, 138 Cardwell Hall, Manhattan, KS 66506 USA

[2] Steklov Inst Math St Petersburg, Fontanka 27, St Petersburg 191023, Russia

来源：

PUBLICATIONS MATHEMATIQUES DE L IHES | 2015年 / 122期

基金：

俄罗斯科学基金会; 美国国家科学基金会;

关键词：

REDUCTIVE GROUP SCHEMES; HOMOGENEOUS SPACES;

D O I：

10.1007/s10240-015-0075-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a regular local ring containing an infinite 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. In other words, if K is the fraction field of R, then the map of non-abelian cohomology pointed sets H-et(1)(R, G) -> H-et(1)(K, G) induced by the inclusion of R into K has a trivial kernel.

引用

页码：169 / 193

页数：25

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