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Universal triviality of the Chow group of 0-cycles and the Brauer group

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 Publication date 2018
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and research's language is English




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We prove that a smooth proper universally CH_0-trivial variety X over a field k has universally trivial Brauer group. This fills a gap in the literature concerning the p-torsion of the Brauer group when k has characteristic p.



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Classifying elements of the Brauer group of a variety X over a p-adic field according to the p-adic accuracy needed to evaluate them gives a filtration on Br X. We show that, on the p-torsion, this filtration coincides with a modified version of that defined by Katos Swan conductor, and that the refined Swan conductor controls how the evaluation maps vary on p-adic discs, giving a geometric characterisation of the refined Swan conductor. We give applications to the study of rational points on varieties over number fields.
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