Varieties with prescribed finite unramified Brauer groups and subgroups precisely obstructing the Hasse principle

Abstract: On varieties defined over number fields, we consider obstructions to the Hasse principle given by subgroups of their Brauer groups. Given an arbitrary pair of non-zero finite abelian groups $B_0\subset B$, we prove the existence of a variety $X$ such that its unramified Brauer group is isomorphic to $B$ and moreover $B_0$ is the smallest subgroup of $B$ that obstructs the Hasse principle. The concerned varieties are normic bundles over the projective line.