Manar Riman
Published 2019-07-20Version 1
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.
On Brauer groups of double covers of ruled surfaces
Geometry of the del Pezzo surface y^2=x^3+Am^6+Bn^6
Finiteness of Brauer groups of K3 surfaces in characteristic 2
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