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

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Auel–Bigazzi–Böhning–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 étale 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.

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Acknowledgements

The author would like to thank Tomoyuki Abe for having fruitful discussions and giving helpful comments. The author is grateful to referees for giving comments and suggestions. The author is supported by JSPS KAKENHI Grant (JP19J00366, JP21K20334).

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  1. Department of Mathematics, School of Engineering, Tokyo Denki University, 5 Senju Asahi Adachi, Tokyo, 120-8551, Japan

    Shusuke Otabe

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  1. Shusuke Otabe
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Correspondence to Shusuke Otabe.

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Otabe, S. On the mod p unramified cohomology of varieties having universally trivial Chow group of zero-cycles. manuscripta math. 171, 215–239 (2023). https://doi.org/10.1007/s00229-022-01381-3

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