Grothendieck's theorem on non-abelian H2 and local global principles

Flicker Yuval, Z. ; Scheiderer, Claus ; Sujatha, R. (1998) Grothendieck's theorem on non-abelian H2 and local global principles Journal of the American Mathematical Society, 11 (3). pp. 731-750. ISSN 0894-0347

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Official URL: http://www.ams.org/journals/jams/1998-11-03/S0894-...

Abstract

A theorem of Grothendieck asserts that over a perfect field k of cohomological dimension one, all non-abelian H2 -cohomology sets of algebraic groups are trivial. The purpose of this paper is to establish a formally real generalization of this theorem. The generalization - to the context of perfect fields of virtual cohomological dimension one - takes the form of a local-global principle for the H2 -sets with respect to the orderings of the field. This principle asserts in particular that an element in H2 is neutral precisely when it is neutral in the real closure with respect to every ordering in a dense subset of the real spectrum of k. Our techniques provide a new proof of Grothendieck's original theorem. An application to homogeneous spaces over k is also given.

Item Type:Article
Source:Copyright of this article belongs to American Mathematical Society.
ID Code:45253
Deposited On:25 Jun 2011 13:32
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