The p-torsion in the Brauer group in characteristic p as an obstruction to Chow zero universal triviality and rationality questions
Abstract: We establish the p-torsion in the Brauer group of a smooth projective variety over a field of characteristic p as an obstruction to universal CH_0-triviality of that variety. For p=2, we compute this for some (desingularisations of) conic bundles over P^2 in terms of their discriminant profiles. Using the degeneration method by Voisin-Colliot-Thélène-Pirutka-Totaro et al. in an unequal characteristic set-up, this yields new explicit examples of threefold conic bundles, defined over Z, that are not stably rational (over C). We believe this can be extended to yield information for fourfold conic bundles as well. This is joint work with Asher Auel, Alessandro Bigazzi and Hans-Christian von Bothmer.