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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - V. A. Krasnov
TI  - Real algebraic GM$\mathbb Z$-surfaces
JO  - Izvestiya. Mathematics 
PY  - 1998
SP  - 695
EP  - 721
VL  - 62
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a2/
LA  - en
ID  - IM2_1998_62_4_a2
ER  - 
%0 Journal Article
%A V. A. Krasnov
%T Real algebraic GM$\mathbb Z$-surfaces
%J Izvestiya. Mathematics 
%D 1998
%P 695-721
%V 62
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1998_62_4_a2/
%G en
%F IM2_1998_62_4_a2
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/

[1] Kalinin I. O., “Kogomologicheskie kharakteristiki veschestvennykh proektivnykh giperpoverkhnostei”, Algebra i analiz, 3:2 (1991), 91–110 | MR

[2] Krasnov V. A., “Otobrazhenie Albaneze dlya veschestvennykh algebraicheskikh mnogoobrazii”, Matem. zametki, 32:3 (1982), 365–374 | MR | Zbl

[3] Krasnov V. A., “Neravenstva Garnaka–Toma dlya otobrazhenii veschestvennykh algebraicheskikh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 47:2 (1983), 268–297 | MR | Zbl

[4] Krasnov V. A., “Otobrazhenie Albaneze dlya GM$\mathbb Z$-mnogoobrazii”, Matem. zametki, 35:5 (1984), 739–747 | MR | Zbl

[5] Krasnov V. A., “Kharakteristicheskie klassy vektornykh rassloenii na veschestvennom algebraicheskom mnogoobrazii”, Izv. AN SSSR. Ser. matem., 55:4 (1991), 716–746 | MR

[6] Krasnov V. A., “O klassakh kogomologii, opredelennykh veschestvennymi tochkami veschestvennoi algebraicheskoi GM-poverkhnosti”, Izv. RAN. Ser. matem., 57:5 (1993), 210–221 | MR | Zbl

[7] Krasnov V. A., “Ob ekvivariantnykh kogomologiyakh Grotendika veschestvennogo algebraicheskogo mnogoobraziya i ikh prilozheniyakh”, Izv. RAN. Ser. matem., 58:3 (1994), 36–52 | MR | Zbl

[8] Krasnov V. A., “Kogomologicheskaya gruppa Brauera veschestvennogo algebraicheskogo mnogoobraziya”, Izv. RAN. Ser. matem., 60:5 (1996), 57–88 | MR | Zbl

[9] Krasnov V. A., “Ekvivariantnye kogomologii veschestvennoi algebraicheskoi poverkhnosti i ikh prilozheniya”, Izv. RAN. Ser. matem., 60:6 (1996), 101–126 | MR | Zbl

[10] Krasnov V. A., “O gruppe Brauera veschestvennoi algebraicheskoi poverkhnosti”, Matem. zametki, 60:6 (1996), 935–938 | MR | Zbl

[11] Krasnov V. A., “Veschestvennye algebraicheskie $\mathrm {GM}$-mnogoobraziya”, Izv. RAN. Ser. matem., 62:3 (1998), 39–66 | MR | Zbl

[12] Mangolte P., van Hamel J., “Algebraic cycles and topology of real Enriques surfaces”, Compositio Math. (to appear) | Zbl

[13] Nikulin V. V., “Involyutsiya tselochislennykh kvadratichnykh form i ikh prilozheniya k veschestvennoi algebraicheskoi geometrii”, Izv. AN SSSR. Ser. matem., 47:1 (1983), 109–177 | MR

[14] Nikulin V. V., “On the Brauer group of real algebraic surfaces”, Algebraic Geometry and its Applications, Yaroslavl', 1992, 113–136 | MR

[15] Rokhlin V. A., “Sravneniya po modulyu 16 v shestnadtsatoi probleme Gilberta”, Funktsion. analiz i ego prilozh., 6:4 (1972), 58–64 ; 7:2 (1973), 91–92 | MR | Zbl | MR | Zbl