Abstract
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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