Vanishing of degree 3 cohomological invariants

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Black, Rebecca¹ 

[1] Swarthmore Coll, 500 Coll Ave, Swarthmore, PA 19081 USA

关键词: Algebraic geometry;    Cohomological invariant;    Motivic cohomology;    Chow ring;   

DOI  :  10.1016/j.jpaa.2019.106214

来源: Elsevier

【 摘 要 】

For a complex algebraic variety X, we show that triviality of the degree three unramified cohomology H-0 (X, H-3) (occurring on the second page of the Bloch-Ogus spectral sequence [1]) follows from a condition on the integral Chow group CH2 X and the integral cohomology group H-3 (X, Z). In the case that X is an appropriate approximation to the classifying stack BG of a finite p-group G, this result states that the group G has no degree three cohomological invariants. As a corollary we show that the nonabelian groups of order p(3) for odd prime p have no degree three cohomological invariants. (C) 2019 Published by Elsevier B.V.

【 授权许可】

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