Geodesic
𝑅-equivalence in spinor groups
Chernousov, Vladimir 1   ; Merkurjev, Alexander 2
1 Fakultät Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
2 Department of Mathematics, University of California, Los Angeles, California 90095-1555
Journal of the American Mathematical Society, Tome 14 (2001) no. 3, pp. 509-534 Cet article a éte moissonné depuis la source American Mathematical Society

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The groups of $R$-equivalent classes of the spinor groups of non-degenerate quadratic forms over arbitrary fields are computed in terms of certain $K$-cohomology groups of corresponding quadric hypersurfaces. As an application, examples of non-rational spinor groups of every dimension $\geq 6$ are given.
DOI : 10.1090/S0894-0347-01-00365-4

Chernousov, Vladimir  1   ; Merkurjev, Alexander  2

1 Fakultät Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany
2 Department of Mathematics, University of California, Los Angeles, California 90095-1555 
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Chernousov, Vladimir; Merkurjev, Alexander. 𝑅-equivalence in spinor groups. Journal of the American Mathematical Society, Tome 14 (2001) no. 3, pp. 509-534. doi: 10.1090/S0894-0347-01-00365-4

[1] Borel, Armand Linear algebraic groups 1991

[2] Chernousov, V., Merkurjev, A. 𝑅-equivalence and special unitary groups J. Algebra 1998 175 198

[3] Colliot-Thélène, Jean-Louis, Sansuc, Jean-Jacques La 𝑅-équivalence sur les tores Ann. Sci. École Norm. Sup. (4) 1977 175 229

[4] Colliot-Thélène, Jean-Louis, Ojanguren, Manuel Espaces principaux homogènes localement triviaux Inst. Hautes Études Sci. Publ. Math. 1992 97 122

[5] Draxl, P. K. Skew fields 1983

[6] Gille, Philippe Un théorème de finitude arithmétique sur les groupes réductifs C. R. Acad. Sci. Paris Sér. I Math. 1993 701 704

[7] Gille, Philippe La 𝑅-équivalence sur les groupes algébriques réductifs définis sur un corps global Inst. Hautes Études Sci. Publ. Math. 1997

[8] Horn, J. Über eine hypergeometrische Funktion zweier Veränderlichen Monatsh. Math. Phys. 1939 359 379

[9] Knus, Max-Albert, Merkurjev, Alexander, Rost, Markus, Tignol, Jean-Pierre The book of involutions 1998

[10] Manin, Yu. I., Hazewinkel, M. Cubic forms: algebra, geometry, arithmetic 1974

[11] Merkurjev, A. S. Generic element in 𝑆𝐾₁ for simple algebras 𝐾-Theory 1993 1 3

[12] Merkurjev, A. S. 𝑅-equivalence and rationality problem for semisimple adjoint classical algebraic groups Inst. Hautes Études Sci. Publ. Math. 1996

[13] Merkurjev, A. S. 𝐾-theory and algebraic groups 1998 43 72

[14] Merkurjev, Alexander Invariants of algebraic groups J. Reine Angew. Math. 1999 127 156

[15] Merkurjev, A. S., Suslin, A. A. The group of 𝐾₁-zero-cycles on Severi-Brauer varieties Nova J. Algebra Geom. 1992 297 315

[16] Milnor, John Algebraic 𝐾-theory and quadratic forms Invent. Math. 1969/70 318 344

[17] Platonov, V. P. Birational properties of spinor varieties Trudy Mat. Inst. Steklov. 1981

[18] Rost, Markus Chow groups with coefficients Doc. Math. 1996

[19] Sherman, Clayton C. 𝐾-cohomology of regular schemes Comm. Algebra 1979 999 1027

[20] Sherman, Clayton Some theorems on the 𝐾-theory of coherent sheaves Comm. Algebra 1979 1489 1508

[21] Suslin, A. A. 𝑆𝐾₁ of division algebras and Galois cohomology 1991 75 99

[22] Swan, Richard G. 𝐾-theory of quadric hypersurfaces Ann. of Math. (2) 1985 113 153

[23] Tao, David A variety associated to an algebra with involution J. Algebra 1994 479 520

[24] Voskresenskiĭ, V. E. Algebraicheskie tory 1977 223

[25] Weil, André Algebras with involutions and the classical groups J. Indian Math. Soc. (N.S.) 1960

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