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.
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.
Let $k$ be a field and $X/k$ be a smooth quasiprojective orbifold. Let $Xto underline{X}$ be its coarse moduli space. In this paper we study the Brauer group of $X$ and compare it with the Brauer group of the smooth locus of $underline{X}$.
We show how the notion of the transcendence degree of a zero-cycle on a smooth projective variety X is related to the structure of the motive M(X). This can be of particular interest in the context of Blochs conjecture, especially for Godeaux surface
s, when the surface is given as a finite quotient of a suitable quintic in P^3.
Asher Auel
,Alessandro Bigazzi
,Christian Bohning
.
(2018)
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"Universal triviality of the Chow group of 0-cycles and the Brauer group"
.
Christian B\\\"ohning
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