Geodesic
Stable cohomology of groups and algebraic varieties
Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 1-21 
F. A. Bogomolov. Stable cohomology of groups and algebraic varieties. Sbornik. Mathematics, Tome 76 (1993) no. 1, pp. 1-21. http://geodesic.mathdoc.fr/item/SM_1993_76_1_a0/
@article{SM_1993_76_1_a0,
     author = {F. A. Bogomolov},
     title = {Stable cohomology of groups and algebraic varieties},
     journal = {Sbornik. Mathematics},
     pages = {1--21},
     year = {1993},
     volume = {76},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_76_1_a0/}
}
TY  - JOUR
AU  - F. A. Bogomolov
TI  - Stable cohomology of groups and algebraic varieties
JO  - Sbornik. Mathematics
PY  - 1993
SP  - 1
EP  - 21
VL  - 76
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1993_76_1_a0/
LA  - en
ID  - SM_1993_76_1_a0
ER  - 
%0 Journal Article
%A F. A. Bogomolov
%T Stable cohomology of groups and algebraic varieties
%J Sbornik. Mathematics
%D 1993
%P 1-21
%V 76
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1993_76_1_a0/
%G en
%F SM_1993_76_1_a0

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

The notion of stable cohomology of algebraic varieties and, based on it, the analogous concept for finite and profinite groups are introduced. It is proved that the ordinary and stable cohomology coincide for the Galois group of the algebraic closure of a function field with an algebraically closed constant field of characteristic zero, and also that the unramified cohomology of this Galois group with coefficients in a module with trivial group action coincides with the unramified cohomology groups of a variety having a given field of rational functions.

[1] Bogomolov F. A., Bloch's conjecture for torsion cohomology of algebraic varieties, Amsterdam University preprint R'85-20, 1985

[2] Bogomolov F. A., Stable cohomology, Max Planck Institute preprint, 1986

[3] Bogomolov F. A., “Gruppa Brauera faktorprostranstv lineinykh predstavlenii”, Izv. AN SSSR. Ser. matem., 51:3 (1987), 485–516 | Zbl

[4] Bogomolov F. A., “Abelevy podgruppy grupp Galua”, Izv. AN SSSR. Ser. matem., 55:1 (1991), 32–67 | MR

[5] Colliot-Thèlène J.-L., Ojanguren M., “Varietè unirationelles non rationelles: au delà de l'example d'Artin et Mumford”, Invent. Math., 97 (1980), 141–158 | DOI | MR

[6] Bloch S., Kato K., “p-adic etale cohomology”, Publ. Math. IHES, 63 (1984), 107–152 | MR

[7] Esnault H., Viehweg E., “Logarithmic De-Rham complexes and vanishing theorems”, Invent. Math., 86 (1986), 161–194 | DOI | MR | Zbl

[8] Colliot-Thèlène J.-L., Parimala R., “Real components of algebraic varieties and etale cohomology”, Invent. Math., 101 (1990), 81–99 | DOI | MR | Zbl

[9] Vasilev V. A., “Topologicheskaya slozhnost algoritmov priblizhennogo resheniya sistem uravnenii”, Algebra i analiz, 1:6 (1989), 98–113