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Vanishing of the Brauer group of a del Pezzo surface of degree 4 (1907.08810v1)
Published 20 Jul 2019 in math.NT and math.AG
Abstract: We explicitly construct a del Pezzo surface $X$ of degree 4 over a field $k$ such that $\operatorname{H}1(k,\operatorname{Pic}\overline X)$ is isomorphic to $\mathbb{ZZ}/2\mathbb{Z}$ while $\operatorname{Br} X/\operatorname{Br} k$ is trivial. This proves that the algorithm to compute the Brauer group in [VAV] cannot be generalized in some cases.