Annals of K-Theory

Chow groups of some generically twisted flag varieties

Nikita Karpenko

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Abstract

We classify the split simple affine algebraic groups G of types A and C over a field with the property that the Chow group of the quotient variety EP is torsion-free, where P G is a special parabolic subgroup (e.g., a Borel subgroup) and E is a generic G-torsor (over a field extension of the base field). Examples of G include the adjoint groups of type A. Examples of EP include the Severi–Brauer varieties of generic central simple algebras.

Article information

Source
Ann. K-Theory, Volume 2, Number 2 (2017), 341-356.

Dates
Received: 15 February 2016
Revised: 26 April 2016
Accepted: 11 May 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.akt/1510841646

Digital Object Identifier
doi:10.2140/akt.2017.2.341

Mathematical Reviews number (MathSciNet)
MR3590349

Zentralblatt MATH identifier
1362.14006

Subjects
Primary: 14C25: Algebraic cycles 20G15: Linear algebraic groups over arbitrary fields

Keywords
central simple algebras algebraic groups projective homogeneous varieties Chow groups

Citation

Karpenko, Nikita. Chow groups of some generically twisted flag varieties. Ann. K-Theory 2 (2017), no. 2, 341--356. doi:10.2140/akt.2017.2.341. https://projecteuclid.org/euclid.akt/1510841646


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References

  • M. Artin, “Brauer–Severi varieties”, pp. 194–210 in Brauer groups in ring theory and algebraic geometry (Wilrijk, Belgium, 1981), edited by F. M. J. van Oystaeyen and A. H. M. J. Verschoren, Lecture Notes in Math. 917, Springer, Berlin, 1982.
  • V. Chernousov and A. Merkurjev, “Connectedness of classes of fields and zero-cycles on projective homogeneous varieties”, Compos. Math. 142:6 (2006), 1522–1548.
  • D. Edidin and W. Graham, “Equivariant intersection theory”, Invent. Math. 131:3 (1998), 595–634.
  • R. Elman, N. Karpenko, and A. Merkurjev, The algebraic and geometric theory of quadratic forms, American Mathematical Society Colloquium Publications 56, Amer. Math. Soc., Providence, RI, 2008.
  • M. Hall, Jr., The theory of groups, Macmillan, New York, 1959.
  • N. A. Karpenko, “Grothendieck Chow motives of Severi–Brauer varieties”, Algebra i Analiz 7:4 (1995), 196–213. In Russian; translated in St. Petersburg Math. J. 7:4 (1996) 649–661.
  • N. A. Karpenko, “On topological filtration for Severi–Brauer varieties”, pp. 275–277 in $K$-theory and algebraic geometry: connections with quadratic forms and division algebras (Santa Barbara, CA, 1992), edited by B. Jacob and A. Rosenberg, Proc. Sympos. Pure Math. 58, Amer. Math. Soc., Providence, RI, 1995.
  • N. A. Karpenko, “Codimension $2$ cycles on Severi–Brauer varieties”, $K$-Theory 13:4 (1998), 305–330.
  • N. Karpenko, “Chow ring of generically twisted varieties of complete flags”, preprint, 2016, hook https://sites.ualberta.ca/~karpenko/publ/chepII1.pdf \posturlhook.
  • N. A. Karpenko and A. S. Merkurjev, “Canonical $p$-dimension of algebraic groups”, Adv. Math. 205:2 (2006), 410–433.
  • M.-A. Knus, A. Merkurjev, M. Rost, and J.-P. Tignol, The book of involutions, American Mathematical Society Colloquium Publications 44, Amer. Math. Soc., Providence, RI, 1998.
  • A. S. Merkurjev, I. A. Panin, and A. R. Wadsworth, “Index reduction formulas for twisted flag varieties, I”, $K$-Theory 10:6 (1996), 517–596.
  • I. Panin, Application of $K$-theory in algebraic geometry, Ph.D. thesis, St. Petersburg Department of Steklov Mathematical Institute, 1984.
  • V. V. Petrov, “A generalization of the Chung–Erdős inequality for the probability of a union of events”, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. $($POMI$)$ 341 (2007), 147–150. In Russian; translated in J. Math. Sci. (New York) 147:4 (2007) 6932–6934.
  • V. Petrov, N. Semenov, and K. Zainoulline, “$J$-invariant of linear algebraic groups”, Ann. Sci. Éc. Norm. Supér. $(4)$ 41:6 (2008), 1023–1053.
  • D. Quillen, “Higher algebraic $K$-theory, I”, pp. 85–147 in Algebraic $K$-theory, I: Higher $K$-theories (Seattle, WA, 1972), edited by H. Bass, Lecture Notes in Math. 341, Springer, Berlin, 1973.
  • A. Schofield and M. Van den Bergh, “The index of a Brauer class on a Brauer–Severi variety”, Trans. Amer. Math. Soc. 333:2 (1992), 729–739.
  • J.-P. Serre, “Cohomological invariants, Witt invariants, and trace forms”, pp. 1–100 in Cohomological invariants in Galois cohomology, Univ. Lecture Ser. 28, Amer. Math. Soc., Providence, RI, 2003.
  • A. Smirnov and A. Vishik, “Subtle characteristic classes”, preprint, 2014.
  • N. Yagita, “Algebraic cobordism and flag varieties”, preprint, 2016.