@article{PMIHES_1996__84__189_0, author = {Merkurjev, Alexander S.}, title = {R-equivalence and rationality problem for semisimple adjoint classical algebraic groups}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {189--213}, publisher = {Institut des Hautes \'Etudes Scientifiques}, volume = {84}, year = {1996}, mrnumber = {98d:14055}, zbl = {0884.20029}, language = {en}, url = {http://archive.numdam.org/item/PMIHES_1996__84__189_0/} }
TY - JOUR AU - Merkurjev, Alexander S. TI - R-equivalence and rationality problem for semisimple adjoint classical algebraic groups JO - Publications Mathématiques de l'IHÉS PY - 1996 SP - 189 EP - 213 VL - 84 PB - Institut des Hautes Études Scientifiques UR - http://archive.numdam.org/item/PMIHES_1996__84__189_0/ LA - en ID - PMIHES_1996__84__189_0 ER -
%0 Journal Article %A Merkurjev, Alexander S. %T R-equivalence and rationality problem for semisimple adjoint classical algebraic groups %J Publications Mathématiques de l'IHÉS %D 1996 %P 189-213 %V 84 %I Institut des Hautes Études Scientifiques %U http://archive.numdam.org/item/PMIHES_1996__84__189_0/ %G en %F PMIHES_1996__84__189_0
Merkurjev, Alexander S. R-equivalence and rationality problem for semisimple adjoint classical algebraic groups. Publications Mathématiques de l'IHÉS, Volume 84 (1996), pp. 189-213. http://archive.numdam.org/item/PMIHES_1996__84__189_0/
[1] Tensor products of quaternion algebras, Proc. Amer. Math. Soc., 35 (1972), 65-66. | MR | Zbl
,[2] Hermitian forms II, J. Algebra, 10 (1968), 503-515. | MR | Zbl
,[3] Cohomologische Invarianten quadratischer Formen, J. Algebra, 36 (1975), 448-491. | MR | Zbl
,[4] Hyperbolic Involutions, Math. Z., 214 (1993), 461-476. | MR | Zbl
, , ,[5] Rationality properties of linear algebraic groups II, Tôhoku Math. J., 20 (1968), 443-497. | MR | Zbl
, ,[6] The group of multipliers of the canonical quadratic form and stable rationality of the variety PSO (in Russian), Matematicheskie zametki, 55 (1994), 114-119. | Zbl
,[7] On algebraic group varieties, J. Math. Soc. Jap., 6 (1954), 303-324. | MR | Zbl
,[8] La R-équivalence sur les tores, Ann. scient. Éc. Norm. Sup., 4e série, 10 (1977), 175-230. | Numdam | MR | Zbl
, ,[9] Schémas et Groupes III (SGA 3, t. III), Lecture Notes in Math., No. 153, Springer, Heidelberg, 1970. | Zbl
, ,[10] Sur les multiplicateurs des similitudes, Rend. Circ. Mat. di Palermo, 3 (1954), 398-408. | MR | Zbl
,[11] Quadratic forms under algebraic extensions, Math. Ann., 219 (1976), 21-42. | EuDML | MR | Zbl
, ,[12] R-équivalence et principe de norme et cohomologie galoisienne, C. R. Acad. Sci. Paris, 316 (1993), 315-320. | MR | Zbl
,[13] Clifford algebras for algebras with involution of type D, J. Algebra, 1 (1964), 288-300. | MR | Zbl
,[14] Quadratic and Hermitian Forms over Rings, Grundlehren math. Wiss., 294, Berlin, Springer-Verlag, 1991. | MR | Zbl
,[15] Book of involutions, in preparation. | Zbl
, , , ,[16] Involutions on rank 16 central simple algebras, J. Indian Math. Soc., 57 (1991), 143-151. | MR | Zbl
, , ,[17] On the discriminant of an involution, Bull. Soc. Math. Belgique, Sér. A, 43 (1991), 89-98. | MR | Zbl
, , ,[18] The Algebraic Theory of Quadratic Forms, Benjamin, Reading, Massachusetts, 1973. | MR | Zbl
,[19] Square class groups and Witt rings of central simple algebras, J. Algebra, 154 (1993), 360-376. | MR | Zbl
, ,[20] Cubic forms, Amsterdam, North-Holland, 1974. | Zbl
,[21] Simple algebras and quadratic forms, Math. USSR Izvestia, 38 (1992), 215-221. | MR | Zbl
,[22] Generic element in SK1 for simple algebras, K-theory, 7 (1993), 1-3. | MR | Zbl
,[23] Involutions and algebraic groups, Preprint. Recherches de mathématique, No. 36, Université catholique de Louvain, Louvain-la-Neuve, Belgium (1993).
,[24] Index reduction formulas for twisted flag varieties, I, K-theory, 10 (1996), 517-596. | MR | Zbl
, , ,[25] K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Math. USSR Izvestiya, 21 (1983), 307-340. | Zbl
, ,[26] The multipliers of similitudes and the Brauer group of homogeneous varieties, J. reine angew. Math., 461 (1995), 13-47. | EuDML | MR | Zbl
, ,[27] Algebraic groups and reduced K-theory, Proc. Inter. Congr. Math., V.1. Helsinki, 1978, p. 311-317. | MR | Zbl
,[28] On the problem of rationality of spinor varieties, Soviet Math. Dokl., 20 (1979), 1027-1031. | MR | Zbl
,[29] On the rationality of canonical spinor varieties, Soviet Math. Dokl., 21 (1980), 830-834. | MR | Zbl
, ,[30] Groupe de Brauer et arithmétique des groupes algébriques linéaires sur un corps de nombres, J. reine angew. Math., 327 (1981), 12-80. | EuDML | MR | Zbl
,[31] Quadratic and Hermitian Forms, Grundlehren math. Wiss., 270, Berlin, Springer-Verlag, 1985. | MR | Zbl
,[32] The index of a Brauer class on a Brauer-Severi variety, Trans. Amer. Math. Soc., 333 (1992), 729-739. | MR | Zbl
, ,[33] The generalized even Clifford algebra, J. Algebra, 172 (1995), 184-204. | MR | Zbl
,[34] Algèbres indécomposables d'exposant premier, Advances in Math., 65 (1987), 205-228. | MR | Zbl
,[35] A Cassels-Pfister theorem for involutions on central simple algebras, J. Algebra, 181 (1996), 857-875. | MR | Zbl
,[36] Formes quadratiques, groupes orthogonaux et algèbres de Clifford, Invent. Math., 5 (1968), 19-41. | EuDML | MR | Zbl
,[37] Classification of algebraic semisimple groups, in Algebraic Groups and Discontinuous Subgroups (A. BOREL and G. D. MOSTOV, eds), Proc. Symp. Pure Math., IX, Providence, Amer. Math. Soc., 1966, p. 32-62. | MR | Zbl
,[38] Algebraic tori, Nauka, Moscow, 1977, p. 223 (Russian). | Zbl
,[39] Toroidal Fano varieties and root system, Math. USSR Izvestija, 24 (1985), 221-244. | Zbl
, ,[40] Algebras with involutions and the classical groups, J. Indian Math. Soc., 24 (1960), 589-623. | MR | Zbl
,[41] Adèles and algebraic groups, Inst. for Adv. Study, Princeton, 1964.
,[42] Reduced norms of simple algebras over function fields, Proc. Steklov Inst. Math., 183 (1991), 261-269. | MR | Zbl
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