Geodesic
Real algebraic GM$\mathbb Z$-surfaces
Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 695-721

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We prove necessary and sufficient conditions for a real algebraic surface to be a $\operatorname{GM}\mathbb Z$-surface. We calculate the Neron–Severi group $\operatorname{NS}(X)$, the Brauer group $\operatorname{Br}(X)$ and the algebraic cohomology group $H_a^1(X(\mathbb R),\mathbb F_2)$, where $X$ is a real projective surface. We also prove Nikulin's congruence for an arbitrary orientable $M$-surface 
@article{IM2_1998_62_4_a2,
     author = {V. A. Krasnov},
     title = {Real algebraic {GM}$\mathbb Z$-surfaces},
     journal = {Izvestiya. Mathematics },
     pages = {695--721},
     publisher = {mathdoc},
     volume = {62},
     number = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a2/}
}
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V. A. Krasnov. Real algebraic GM$\mathbb Z$-surfaces. Izvestiya. Mathematics , Tome 62 (1998) no. 4, pp. 695-721. http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a2/