[Grassmanniennes incompressibles d'espaces isotropes]
We study 2-incompressible Grassmannians of isotropic subspaces of a quadratic form, of a hermitian form over a quadratic extension of the base field, and of a hermitian form over a quaternion algebra.
Nous étudions des grassmanniennes 2-incompressibles de sous-espaces isotropes d'une forme quadratique ainsi que d'une forme hermitienne au-dessus d'une extension quadratique du corps de base ou au-dessus d'une algèbre de quaternions.
DOI : 10.24033/bsmf.2727
Keywords: Quadratic forms, algebraic groups, projective homogeneous varieties, orthogonal, symplectic, and unitary Grassmannians, Chow groups and motives, canonical dimension and incompressibility.
Mots-clés : Formes quadratiques, groupes algébriques, variétés projectives homogènes, grassmanniennes orthogonales, symplectiques et unitaires, groupes et motifs de Chow, dimension canonique et incompressibilité.
@article{BSMF_2016__144_4_763_0,
author = {Karpenko, Nikita A.},
title = {Incompressible {Grassmannians} of isotropic subspaces},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {763--773},
year = {2016},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {144},
number = {4},
doi = {10.24033/bsmf.2727},
mrnumber = {3562612},
zbl = {1404.14056},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2727/}
}
TY - JOUR AU - Karpenko, Nikita A. TI - Incompressible Grassmannians of isotropic subspaces JO - Bulletin de la Société Mathématique de France PY - 2016 SP - 763 EP - 773 VL - 144 IS - 4 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2727/ DO - 10.24033/bsmf.2727 LA - en ID - BSMF_2016__144_4_763_0 ER -
%0 Journal Article %A Karpenko, Nikita A. %T Incompressible Grassmannians of isotropic subspaces %J Bulletin de la Société Mathématique de France %D 2016 %P 763-773 %V 144 %N 4 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2727/ %R 10.24033/bsmf.2727 %G en %F BSMF_2016__144_4_763_0
Karpenko, Nikita A. Incompressible Grassmannians of isotropic subspaces. Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 4, pp. 763-773. doi: 10.24033/bsmf.2727
The algebraic and geometric theory of quadratic forms, American Mathematical Society Colloquium Publications, 56, Amer. Math. Soc., Providence, RI, 2008, 435 pages (ISBN: 978-0-8218-4329-1) | MR | Zbl | DOI
Intersection theory, Ergebn. Math. Grenzg.. 3. Folge. A Series of Modern Surveys in Mathematics, 2, Springer, Berlin, 1998, 470 pages (ISBN: 3-540-62046-X; 0-387-98549-2) | MR | Zbl | DOI
A numerical invariant for linear representations of finite groups, Comment. Math. Helv., Volume 90 (2015), pp. 667-701 (ISSN: 0010-2571) | MR | Zbl | DOI
Isotropy of unitary involutions, Acta Math., Volume 211 (2013), pp. 227-253 (ISSN: 0001-5962) | MR | Zbl | DOI
A bound for canonical dimension of the (semi)spinor groups, Duke Math. J., Volume 133 (2006), pp. 391-404 (ISSN: 0012-7094) | MR | Zbl | DOI
Canonical dimension, Proceedings of the International Congress of Mathematicians. Volume II, Hindustan Book Agency, New Delhi (2010), pp. 146-161 | MR | Zbl
Sufficiently generic orthogonal Grassmannians, J. Algebra, Volume 372 (2012), pp. 365-375 (ISSN: 0021-8693) | MR | Zbl | DOI
Upper motives of algebraic groups and incompressibility of Severi-Brauer varieties, J. reine angew. Math., Volume 677 (2013), pp. 179-198 (ISSN: 0075-4102) | MR | Zbl
Variations on a theme of rationality of cycles, Cent. Eur. J. Math., Volume 11 (2013), pp. 1056-1067 (ISSN: 1895-1074) | MR | Zbl | DOI
Incompressibility of products of Weil transfers of generalized Severi-Brauer varieties, Math. Z., Volume 279 (2015), pp. 767-777 | MR | Zbl | DOI
Incompressibility of products of pseudo-homogeneous varieties, Canadian Math. Bull. (2016) | MR | Zbl | DOI
Incompressibility of products by Grassmannians of isotropic subspaces (preprint https://www.math.uni-bielefeld.de/lag/man/541.pdf )
Hermitian forms over quaternion algebras, Compos. Math., Volume 150 (2014), pp. 2073-2094 (ISSN: 0010-437X) | MR | Zbl | DOI
The book of involutions, American Mathematical Society Colloquium Publications, 44, Amer. Math. Soc., Providence, RI, 1998, 593 pages (ISBN: 0-8218-0904-0) | MR | Zbl | DOI
Essential dimension: a survey, Transform. Groups, Volume 18 (2013), pp. 415-481 (ISSN: 1083-4362) | MR | Zbl | DOI
Quadratic and Hermitian forms, Grundl. math. Wiss., 270, Springer, Berlin, 1985, 421 pages (ISBN: 3-540-13724-6) | MR | Zbl | DOI
, Geometric methods in the algebraic theory of quadratic forms (Lecture Notes in Math.), Volume 1835, Springer, Berlin, 2004, pp. 25-101 | MR | Zbl | DOI
On the Chow groups of quadratic Grassmannians, Doc. Math., Volume 10 (2005), pp. 111-130 (ISSN: 1431-0635) | MR | Zbl | DOI
Generic points of quadrics and Chow groups, Manuscripta Math., Volume 122 (2007), pp. 365-374 (ISSN: 0025-2611) | MR | Zbl | DOI
, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. II (Progr. Math.), Volume 270, Birkhäuser, 2009, pp. 661-685 | MR | Zbl | DOI
Cité par Sources :
