On the Finiteness of the Brauer Group of an Arithmetic Scheme

The Artin conjecture on the finiteness of the Brauer group is shown to hold for an arithmetic model of a K3 surface over a number field $k$. The Brauer group of an arithmetic model of an Enriques surface over a sufficiently large number field is shown to be a $2$-group. For almost all prime numbers $l$, the triviality of the $l$-primary component of the Brauer group of an arithmetic model of a smooth projective simply connected Calabi–Yau variety $V$ over a number field $k$ under the assumption that $V(k)\neq\varnothing$ is proved.