Grothendieck's theorem on non-abelian H^2 and local-global principles
| dc.creator | Flicker, Yuval Z. | |
| dc.creator | Scheiderer, Claus | |
| dc.creator | Sujatha, R. | |
| dc.date | 1998-03-24 | |
| dc.date.accessioned | 2026-07-07T05:24:11Z | |
| dc.date.available | 2026-07-07T05:24:11Z | |
| dc.description | A theorem of Grothendieck asserts that over a perfect field k of cohomological dimension one, all non-abelian H^2-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 H^2-sets with respect to the orderings of the field. This principle asserts in particular that an element in H^2 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. | |
| dc.description | 22 pages, AMS-TeX; accepted for publication by the Journal of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/9803113 | |
| dc.identifier | http://arxiv.org/abs/math/9803113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76738 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 14L30; 11R34; 12G05 | |
| dc.title | Grothendieck's theorem on non-abelian H^2 and local-global principles | |
| dc.type | text |