Geodesic
On the Brauer group of an arithmetic scheme
Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 357-388

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For an Enriques surface $V$ over a number field $k$ with a $k$-rational point we prove that the $l$-component of $\operatorname{Br}(V)/{\operatorname{Br}(k)}$ is finite if and only if $l\ne 2$. For a regular projective smooth variety satisfying the Tate conjecture for divisors over a number field, we find a simple criterion for the finiteness of the $l$-component of $\operatorname{Br}'(V)/{\operatorname{Br}(k)}$. Moreover, for an arithmetic model $X$ of $V$ we prove a variant of Artin's conjecture on the finiteness of the Brauer group of $X$. Applications to the finiteness of the $l$-components of Shafarevich–Tate groups are given. 
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     author = {S. G. Tankeev},
     title = {On the {Brauer} group of an arithmetic scheme},
     journal = {Izvestiya. Mathematics },
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     number = {2},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a4/}
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S. G. Tankeev. On the Brauer group of an arithmetic scheme. Izvestiya. Mathematics , Tome 65 (2001) no. 2, pp. 357-388. http://geodesic.mathdoc.fr/item/IM2_2001_65_2_a4/