Geodesic
On the Algebraic Cohomology of Real Algebraic $M$-Varieties
Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 854-867.

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

For a real algebraic $M$-variety $X$, the canonical homomorphism of the algebraic cohomology group of the set of real points into the algebraic cohomology group of the set of complex points $$ \varrho_k\colon H_{\operatorname{alg}}^k(X(\mathbb R),\mathbb Z/2)\to H_{\operatorname{alg}}^{2k}(X(\mathbb C),\mathbb Z/2). $$ is considered. This homomorphism agrees with the cycle mappings. Estimates for the dimension of the kernel of this homomorphism are given. 
@article{MZM_2004_76_6_a5,
     author = {V. A. Krasnov},
     title = {On the {Algebraic} {Cohomology} of {Real} {Algebraic} $M${-Varieties}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {854--867},
     publisher = {mathdoc},
     volume = {76},
     number = {6},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a5/}
}
TY  - JOUR
AU  - V. A. Krasnov
TI  - On the Algebraic Cohomology of Real Algebraic $M$-Varieties
JO  - Matematičeskie zametki
PY  - 2004
SP  - 854
EP  - 867
VL  - 76
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a5/
LA  - ru
ID  - MZM_2004_76_6_a5
ER  - 
%0 Journal Article
%A V. A. Krasnov
%T On the Algebraic Cohomology of Real Algebraic $M$-Varieties
%J Matematičeskie zametki
%D 2004
%P 854-867
%V 76
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a5/
%G ru
%F MZM_2004_76_6_a5
V. A. Krasnov. On the Algebraic Cohomology of Real Algebraic $M$-Varieties. Matematičeskie zametki, Tome 76 (2004) no. 6, pp. 854-867. http://geodesic.mathdoc.fr/item/MZM_2004_76_6_a5/

[1] Krasnov V. A., “Kharakteristicheskie klassy vektornykh rassloenii na veschestvennom algebraicheskom mnogoobrazii”, Izv. AN SSSR. Ser. matem., 55:4 (1991), 716–747

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

[3] Krasnov V. A., “Veschestvennye algebraicheskie $GM\mathbb Z$-poverkhnosti”, Izv. RAN. Ser. matem., 62:4 (1998), 51–80 | MR | Zbl

[4] Degtyarev A., Kharlamov V., “Halves of real Enriques surface”, Comment. Math. Helv., 71 (1996), 628–663 | DOI | MR | Zbl

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

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

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

[8] Krasnov V. A., “Etalnye i ekvivariantnye kogomologii veschestvennogo algebraicheskogo mnogoobraziya”, Izv. RAN. Ser. matem., 62:5 (1998), 166–186 | MR