On the mod $p$ unramified cohomology of varieties having universally trivial Chow group of zero-cycles

DOI10.1007/S00229-022-01381-3arXiv2010.03808MaRDI QIDQ6350798

Shusuke Otabe

Publication date: 8 October 2020

Abstract: Auel-Bigazzi-B"ohning-Graf von Bothmer proved that if a proper smooth variety $X$ over a field $k$ of characteristic $p>0$ has universally trivial Chow group of $0$-cycles, the cohomological Brauer group of $X$ is universally trivial as well. In this paper, we generalize their argument to arbitrary unramified mod $p$ 'etale motivic cohomology groups. We also see that the properness assumption on the variety $X$ can be dropped off by using the Suslin homology together with a certain tame subgroup of the unramified cohomology group.

Mathematics Subject Classification ID

Brauer groups of schemes (14F22) (Equivariant) Chow groups and rings; motives (14C15) Motivic cohomology; motivic homotopy theory (14F42) Rationality questions in algebraic geometry (14E08)

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