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Grothendieck's theorem on non-abelian H 2 and local-global principles

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1998

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Flicker, Yuval Z.
Sujatha, Ramdorai

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Journal of the American Mathematical Society. 1998, 11(03), pp. 731-751. ISSN 0894-0347. eISSN 1088-6834. Available under: doi: 10.1090/S0894-0347-98-00271-9

Zusammenfassung

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.

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510 Mathematik

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ISO 690FLICKER, Yuval Z., Claus SCHEIDERER, Ramdorai SUJATHA, 1998. Grothendieck's theorem on non-abelian H 2 and local-global principles. In: Journal of the American Mathematical Society. 1998, 11(03), pp. 731-751. ISSN 0894-0347. eISSN 1088-6834. Available under: doi: 10.1090/S0894-0347-98-00271-9
BibTex
@article{Flicker1998Groth-23308,
  year={1998},
  doi={10.1090/S0894-0347-98-00271-9},
  title={Grothendieck's theorem on non-abelian H 2 and local-global principles},
  number={03},
  volume={11},
  issn={0894-0347},
  journal={Journal of the American Mathematical Society},
  pages={731--751},
  author={Flicker, Yuval Z. and Scheiderer, Claus and Sujatha, Ramdorai}
}
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