The Brauer group and the Brauer-Manin set of products of varieties

Alexei N. Skorobogatov, Yuri G. Zarhin

Let $X$ and $Y$ be smooth and projective varieties over a field $k$ finitely generated over $\mathbb{Q}$, and let $\ov X$ and $\ov Y$ be the varieties over an algebraic closure of $…