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Maximal indexes of flag varieties for spin groups

Part of: Linear algebraic groups and related topics Cycles and subschemes

Published online by Cambridge University Press:  26 April 2021

Rostislav A. Devyatov ,
Nikita A. Karpenko  and
Alexander S. Merkurjev
Rostislav A. Devyatov
Affiliation:
Max-Planck-Institut für Mathematik, Bonn, Germany; E-mail: deviatov@mccme.ru
Nikita A. Karpenko
Affiliation:
Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada; E-mail: karpenko@ualberta.ca
Alexander S. Merkurjev
Affiliation:
Department of Mathematics, University of California, Los Angeles, USA; E-mail: merkurev@math.ucla.edu

Abstract

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We establish the sharp upper bounds on the indexes for most of the twisted flag varieties under the spin groups ${\operatorname {\mathrm {Spin}}(n)}$.

MSC classification

Primary: 20G15: Linear algebraic groups over arbitrary fields
Secondary: 14C25: Algebraic cycles
Type
Algebraic and Complex Geometry
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e34
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Borel, A., Linear Algebraic Groups, second edn, Graduate Texts in Mathematics, 126 (Springer-Verlag, New York, 1991).10.1007/978-1-4612-0941-6CrossRefGoogle Scholar
Chernousov, V. and Merkurjev, A., ‘Essential dimension of spinor and Clifford groups’, Algebra Number Theory 8(2) (2014), 457–472.10.2140/ant.2014.8.457CrossRefGoogle Scholar
Demazure, M., ‘Automorphismes et déformations des variétés de Borel’, Invent. Math. 39(2) (1977), 179–186.10.1007/BF01390108CrossRefGoogle Scholar
Edidin, D. and Graham, W., ‘Characteristic classes in the Chow ring’, J. Algebraic Geom. 6(3) (1997), 431–443.Google Scholar
Edidin, D. and Graham, W., ‘Equivariant intersection theory’, Invent. Math. 131(3) (1998), 595–634.10.1007/s002220050214CrossRefGoogle Scholar
Elman, R., Karpenko, N. and Merkurjev, A., The Algebraic and Geometric Theory of Quadratic Forms, American Mathematical Society Colloquium Publications, 56 (American Mathematical Society, Providence, RI, 2008).Google Scholar
Karpenko, N. A., ‘A bound for canonical dimension of the (semi)spinor groups’, Duke Math. J. 133(2) (2006), 391–404.10.1215/S0012-7094-06-13328-8CrossRefGoogle Scholar
Karpenko, N. A., ‘Unitary Grassmannians’, J. Pure Appl. Algebra 216(12) (2012), 2586–2600.10.1016/j.jpaa.2012.03.024CrossRefGoogle Scholar
Karpenko, N. A., ‘Around 16-dimensional quadratic forms in ${I}_q^3$’, Math. Z. 285(1-2) (2017), 433–444.10.1007/s00209-016-1714-xCrossRefGoogle Scholar
Karpenko, N. A., ‘On generic quadratic forms’, Pacific J. Math. 297(2) (2018), 367–380.10.2140/pjm.2018.297.367CrossRefGoogle Scholar
Karpenko, N. A., ‘On generically split generic flag varieties’, Bull. Lond. Math. Soc. 50 (2018), 496–508.10.1112/blms.12161CrossRefGoogle Scholar
Karpenko, N. A. and Merkurjev, A. S., ‘Canonical $p$-dimension of algebraic groups’, Adv. Math. 205(2) (2006), 410–433.10.1016/j.aim.2005.07.013CrossRefGoogle Scholar
Primozic, E., ‘Motivic Steenrod operations in characteristic p’, Forum Math. Sigma 8 (2020), e52.10.1017/fms.2020.34CrossRefGoogle Scholar
Totaro, B., ‘The Chow ring of a classifying space’, In Algebraic $K$-theory (Seattle, WA, 1997), Proceedings of Symposia in Applied Mathematics, 67 (American Mathematical Society, Providence, RI, 1999), 249–281.Google Scholar
Totaro, B., ‘The torsion index of the spin groups’, Duke Math. J. 129(2) (2005), 249–290.Google Scholar
Vishik, A., ‘Motives of quadrics with applications to the theory of quadratic forms’, in Geometric Methods in the Algebraic Theory of Quadratic Forms, Lecture Notes in Mathematics, 1835 (Springer, Berlin, 2004), 25–101.10.1007/978-3-540-40990-8_2CrossRefGoogle Scholar
Vishik, A., ‘On the Chow groups of quadratic Grassmannians’, Doc. Math. 10 (2005), 111–130.Google Scholar
Vishik, A., ‘Fields of $u$-invariant ${2}^r+1$’, in Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin. Vol. II, Progress in Mathematics, 270 (Birkhäuser Boston Inc., Boston, MA, 2009), 661–685.10.1007/978-0-8176-4747-6_22CrossRefGoogle Scholar