Unramified cohomology of classifying varieties for classical simply connected groups
Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 35 (2002) no. 3, p. 445-476
@article{ASENS_2002_4_35_3_445_0,
     author = {Merkurjev, Alexander},
     title = {Unramified cohomology of classifying varieties for classical simply connected groups},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 35},
     number = {3},
     year = {2002},
     pages = {445-476},
     doi = {10.1016/s0012-9593(02)01097-2},
     zbl = {1022.14015},
     mrnumber = {1914006},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2002_4_35_3_445_0}
}
Merkurjev, Alexander. Unramified cohomology of classifying varieties for classical simply connected groups. Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 35 (2002) no. 3, pp. 445-476. doi : 10.1016/s0012-9593(02)01097-2. http://www.numdam.org/item/ASENS_2002_4_35_3_445_0/

[1] Blanchet A., Function fields of generalized Brauer-Severy varieties, Comm. Algebra 19 (1991) 97-118. | MR 1092553 | Zbl 0717.16014

[2] Bogomolov F.A., Brauer groups of the fields of invariants of algebraic groups, Mat. Sb. 180 (2) (1989) 279-293. | MR 993459 | Zbl 0759.14008

[3] Bourbaki N., Groupes et Algèbres de Lie, Chap. 4, 5, 6, Masson, Paris, 1981. | MR 647314 | Zbl 0483.22001

[4] Colliot-Thélène J.-L., Sansuc J.-J., The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group), Notes from the 1988 ELAM conference, Santiago de Chile, http://www.math.u-psud.fr/~colliot/liste-publi.html.

[5] Colliot-Thélène J.-L., Birational invariants purity, and the Gersten conjecture purity, in: Jacob W., Rosenberg A. (Eds.), Proceedings of the 1992 Summer Research Institute on Quadratic Forms and Division Algebras, Symposia Pure Math., 58.1, American Mathematical Society, Providence, RI, 1995, pp. 1-64. | MR 1327280 | Zbl 0834.14009

[6] Demazure M., Grothendieck A., Schémas et Groupes III (SGA 3, Tome III), Lect. Notes in Math., 153, Springer, Heidelberg, 1970. | MR 274458

[7] Esnault H., Kahn B., Levine M., Viehweg E., The Arason invariant and mod 2 algebraic cycles, J. Amer. Math. Soc. 11 (1) (1998) 73-118. | MR 1460391 | Zbl 1025.11009

[8] Garibaldi R., Tignol J.-P., Wadsworth A., Galois cohomology of special orthogonal groups, Manuscripta Math. 93 (2) (1997) 247-266. | MR 1464368 | Zbl 1055.11512

[9] Knus M.-A., Merkurjev A.S., Rost M., Tignol J.-P., The Book of Involutions, American Mathematical Society Colloquium Publications, 44, American Mathematical Society, Providence, RI, 1998. | MR 1632779 | Zbl 0955.16001

[10] Lam T.-Y., The Algebraic Theory of Quadratic Forms, Benjamin, Reading, MA, 1973. | MR 396410 | Zbl 0259.10019

[11] Merkurjev A.S., Invariants of algebraic groups, J. Reine Angew. Math. 508 (1999) 127-156. | MR 1676873 | Zbl 0913.16010

[12] Merkurjev A.S., Panin I.A., Wadsworth A., Index reduction formulas for twisted flag varieties, II, 14 (2) (1998) 101-196. | MR 1628279 | Zbl 0918.16013

[13] Rost M., Chow groups with coefficients, Documenta Mathematica 1 (1996) 319-393. | MR 1418952 | Zbl 0864.14002

[14] Saltman D., The Brauer group and the center of generic matrices, J. Algebra 97 (1) (1985) 53-67. | MR 812169 | Zbl 0586.13005

[15] Saltman D., Invariant fields of linear groups and division algebras, in: Perspectives in Ring Theory (Antwerp, 1987), Kluwer Academic, 1988, pp. 279-297. | MR 1048416 | Zbl 0688.16020

[16] Saltman D., Brauer groups of invariant fields, geometrically negligible classes, an equivariant Chow group, and unramified H3, in: Jacob W., Rosenberg A. (Eds.), Proceedings of the 1992 Summer Research Institute on Quadratic Forms and Division Algebras, Symposia Pure Math., 58.1, American Mathematical Society, Providence, RI, 1995, pp. 189-246. | MR 1327283 | Zbl 0827.13003

[17] Saltman D., The Schur index and Moody's theorem, 7 (1993) 309-332. | MR 1246280 | Zbl 0801.16014

[18] Serre J.-P., Letter to M. Rost, Harvard, Dec. 3, 1992.

[19] Serre J.-P., Cohomologie galoisienne, Lect. Notes Math., 5, Springer-Verlag, Berlin, 1994. | MR 1324577 | Zbl 0812.12002

[20] Serre J.-P., Cohomologie galoisienne: progrès et problèmes, Séminaire Bourbaki, Vol. 1993/94, Astérisque (1995), no. 227, Exp. No. 783, 4, 229-257. | Numdam | MR 1321649 | Zbl 0837.12003

[21] Tits J., Classification of algebraic semisimple groups, in: Borel A., Mostow G.D. (Eds.), Algebraic Groups and Discontinuous Subgroups, Proc. Symp. Pure Math., 9, 1966, pp. 33-62. | MR 224710 | Zbl 0238.20052

[22] Tits J., Représentations linéaires irréductibles d'un groupe réductif sur un corps quelconque, J. Reine Angew. Math. 247 (1971) 196-220. | MR 277536 | Zbl 0227.20015

[23] Zariski O., Samuel P., Commutative Algebra. II, Graduate Texts in Mathematics, 29, Springer-Verlag, 1975. | Zbl 0313.13001