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Incompressibility of quadratic Weil transfer of generalized Severi–Brauer varieties

Part of: Algebraic groups

Published online by Cambridge University Press:  12 May 2011

Nikita A. Karpenko
Nikita A. Karpenko
Affiliation:
Université Pierre et Marie Curie Paris 06, Institut de Mathématiques de Jussieu, F-75252 Paris, France (karpenko@math.jussieu.fr)
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Abstract

Let X be the variety obtained by the Weil transfer with respect to a quadratic separable field extension of a generalized Severi–Brauer variety. We study (and, in some cases, determine) the canonical dimension, incompressibility, and motivic indecomposability of X. We determine the canonical 2-dimension of X (in the general case).

Keywords

algebraic groupsprojective homogeneous varietiesChow groups

MSC classification

Secondary: 14L17: Affine algebraic groups, hyperalgebra constructions
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 11 , Issue 1 , January 2012 , pp. 119 - 131
Copyright
Copyright © Cambridge University Press 2011

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References

1.Berhuy, G. and Reichstein, Z., On the notion of canonical dimension for algebraic groups, Adv. Math. 198(1) (2005), 128–171.CrossRefGoogle Scholar
2.Brosnan, P., On motivic decompositions arising from the method of Białynicki–Birula, Invent. Math. 161(1) (2005), 91–111.CrossRefGoogle Scholar
3.Chernousov, V. and Merkurjev, A., Motivic decomposition of projective homogeneous varieties and the Krull–Schmidt theorem, Transform. Groups 11(3) (2006), 371–386.Google Scholar
4.Chernousov, V., Gille, S. and Merkurjev, A., Motivic decomposition of isotropic projective homogeneous varieties, Duke Math. J. 126(1) (2005), 137–159.Google Scholar
5.Elman, R., Karpenko, N., and Merkurjev, A., The algebraic and geometric theory of quadratic forms, American Mathematical Society Colloquium Publications, Volume 56 (American Mathematical Society, Providence, RI, 2008).Google Scholar
6.Karpenko, N. A., Grothendieck Chow motives of Severi–Brauer varieties, Algebra I Analiz 7(4) (1995), 196–213.Google Scholar
7.Karpenko, N. A., Cohomology of relative cellular spaces and of isotropic flag varieties, Algebra I Analiz 12(1) (2000), 3–69.Google Scholar
8.Karpenko, N. A., Weil transfer of algebraic cycles, Indagationes Math. 11(1) (2000), 73–86.Google Scholar
9.Karpenko, N. A., Upper motives of algebraic groups and incompressibility of Severi–Brauer varieties, preprint (arXiv:0904.2844v2; 2009).Google Scholar
10.Karpenko, N. A., Hyperbolicity of orthogonal involutions, Doc. Math. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010), 371–389 (electronic).Google Scholar
11.Karpenko, N. A., Upper motives of outer algebraic groups, In Quadratic forms, linear algebraic groups, and cohomology, Developments in Mathematics, Volume 18, pp. 249–258 (Springer, 2010).Google Scholar
12.Karpenko, N. A. and Merkurjev, A. S., Canonical p-dimension of algebraic groups, Adv. Math. 205(2) (2006), 410–433.CrossRefGoogle Scholar
13.Karpenko, N. A. and Merkurjev, A. S., Essential dimension of finite p-groups, Invent. Math. 172(3) (2008), 491–508.CrossRefGoogle Scholar
14.Knus, M.-A., Merkurjev, A., Rost, M. and Tignol, J.-P., The book of involutions (with a preface in French by J. Tits), American Mathematical Society Colloquium Publications, Volume 44 (American Mathematical Society, Providence, RI, 1998).Google Scholar
15.Merkurjev, A. S., Essential dimension, In Quadratic forms—algebra, arithmetic, and geometry, Contemporary Mathematics, Volume 493, pp. 299–326 (American Mathematical Society, Providence, RI, 2009).CrossRefGoogle Scholar
16.Schofield, A. and Van den Bergh, M., The index of a Brauer class on a Brauer–Severi variety, Trans. Am. Math. Soc. 333(2) (1992), 729–739.Google Scholar
17.Zhykhovich, M., Motivic decomposability of generalized Severi–Brauer varieties, C. R. Acad. Sci. Paris Sér. I 348(17–18) (2010), 989–992.Google Scholar