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) not equal empty set is proved.