Publications of Nikita Karpenko

• (with Charles De Clercq and Anne Quéguiner-Mathieu)
  A-upper motives
  Current inofficial version (23 Apr 2024, 23 pages).
  Most recent official version (14/16 Mar 2024, 19 pages).

• (with Curtis R. Harvey)
  Quadratic forms in Iⁿ of dimension 2ⁿ+2^n-1
  Preprint (10 Mar 2024, 5 pages).

• (with an appendix by Alexander S. Merkurjev)
  Finite extensions partially splitting PGO-torsors
  To appear in Math. Res. Lett.
  Final preprint version (18 Nov 2023, 21 pages).

• On Spin(2023)-torsors
  New York J. Math. 30 (2024), 550--560.
  Final preprint version (28 Feb 2024, 10 pages).
  CAUTION: numbering of statements in the journal version differs from the preprint.

• On isotropy fields of Spin(18)-torsors
  To appear in St. Petersburg Math. J.
  Final preprint version (28 Aug 2023, 7 pages).

• On special Clifford groups and their characteristic classes
  To appear in Ric. Mat.
  Final preprint version (4 Dec 2023, 20 pages).

• On characteristic classes modulo torsion for spin groups
  To appear in J. Algebra Appl.
  Final preprint version (29 Feb 2024, 13 pages).

• Notes on spin grassmannians
  Preprint (20 Oct 2022, 7 pages).
  Not intended for a journal submission.

• Chow ring of BSO(2n) in characteristic 2
  To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (5).
  Final preprint version (19 Oct 2022, 11 pages).

• Filtrations on the representation ring of an affine algebraic group
  Q. J. Math. 74 (2023), 811--824.
  Final preprint version (21 Dec 2022, 14 pages).

• Envelopes and classifying spaces
  Math. Nachr. 296 (2023), 4769--4777.
  Final preprint version (11 Dec 2022, 10 pages).

• On classifying spaces of spin groups
  Results Math. 77 (2022), no. 4, paper no. 144, 8 pages.
  Final preprint version (14 May 2022, 7 pages).
  Correction: in the bottom line of the commutative square preceding Remark 6
  the following letters should be removed: "f" and both appearances of "W".
  Erratum: see Appendix in On characteristic classes modulo torsion for spin groups posted above.

• (with A. Merkurjev)
  Poincaré duality for tautological Chern subrings of orthogonal grassmannians
  Math. Scand. 128 (2022), 221--228.
  Final preprint version (6 Dec 2021, 7 pages).
  CAUTION: numbering of statements in the journal version differs from the preprint.

• (with S. Baek)
  Yagita's counter-examples and beyond
  Ark. Mat. 61 (2023), no. 1, 1--17.
  Final reprint version (16 Jun 2022, 13 pages).

• (with A. Merkurjev)
  Indexes of generic grassmannians for spin groups
  Proc. Lond. Math. Soc. (3) 125 (2022), no. 4, 825--840.
  Appendix B has been corrupted by the journal. Please refer to the preprint version:
  Final preprint version (7 May 2022, 15 pages).
  Correction: In the table from Appendix B of the preprint version, for d=17 and for d=18, the first appearance of 3 has to be underlined.

• On generic flag varieties for odd spin groups
  Publ. Mat. 67 (2023), 743--756.
  Final preprint version (23 Nov 2021, 11 pages).

• (with R. A. Devyatov and A. S. Merkurjev)
  Maximal indexes of flag varieties for spin groups
  Forum of Mathematics, Sigma 9 (2021): e34, 1--12.
  doi:10.1017/fms.2021.30

• (with A. S. Merkurjev)
  The Chow ring of the classifying space of the unitary group
  Algebra and Number Theory 16 (2022), no. 1, 139--154.
  Final preprint version (12 Feb 2021, 15 pages).

• (with A. S. Merkurjev)
  Equivariant connective K-theory
  J. Algebraic Geom. 31 (2022), 181--204.
  Final preprint version (30 Jul 2020, 19 pages).

• An ultimate proof of Hoffmann-Totaro's conjecture
  J. Eur. Math. Soc. (JEMS) 24 (2022), no. 12, 4385--4398.
  Final preprint version (14 Dec 2021, 13 pages).

• Extended Petrov-Semenov's connections
  Archiv der Mathematik 115 (2020), 27--34.
  doi: 10.1007/s00013-020-01438-3
  Final preprint version (29 Dec 2019, 7 pages).

• A remark on connective K-theory
  J. Algebra 560 (2020), 1211--1218.
  Final preprint version (4 June 2020, 7 pages).

• A counter-example by Yagita
  International Journal of Mathematics 31 (2020) no. 3, 2050025 (10 pages).
  doi: 10.1142/S0129167X20500251
  Final preprint version (26 Dec 2019, 9 pages).

• (with A. S. Merkurjev)
  Chow filtration on representation rings of algebraic groups
  International Mathematics Research Notices 9 (2021), 6691--6716.
  doi: 10.1093/imrn/rnz049
  Final preprint version (5 February 2018, 20 pages).
  CAUTION: numbering of statements in the journal version differs from the preprint.

• (with E. Mackall and with appendices by E. Mackall)
  On the K-theory coniveau epimorphism for products of Severi-Brauer varieties
  Annals of K-Theory 4 (2019), no. 4, 317--344.
  Final preprint version (19 October 2018, 21 pages).

• On generic flag varieties of Spin(11) and Spin(12)
  Manuscripta Math. 157 (2018), 13--21.
  Final preprint version (28 November 2017, 9 pages).
  Corrected final preprint version (21 March 2018, 9 pages).
  List of corrections

• On generic quadratic forms
  Screen. Print.
  Pacific J. Math. 297 (2018), no. 2, 367--380.
  Correction: [V] should be added in the beginning of the formula in Line 4 of Proof of Theorem 2.1.
  Final preprint version of 29 March 2018, 12 pages.

• On generically split generic flag varieties
  Bull. Lond. Math. Soc. 50 (2018), 496--508.
  Final preprint version, of 10 April 2018, 15 pages.

• Chow ring of generic flag varieties
  Math. Nachr. 290 (2017), 2641--2647.
  Final preprint version (14 February 2017, 9 pages).
  CAUTION: numbering of subsections in the journal version differs from the preprint.

• Chow ring of generically twisted varieties of complete flags
  Adv. Math. 306 (2017), 789--806.
  Final preprint version (11 August 2016, 15 pages).

• Chow groups of some generically twisted flag varieties
  Annals of K-Theory 2 (2017), no. 2, 341--356.
  Final preprint version (26 April 2016, 13 pages).

• Around 16-dimensional quadratic forms in I_q³
  Math. Z. 285 (2017), no. 1, 433--444.
  Final preprint version (4 June 2016, 13 pages).

• Incompressibility of products of pseudo-homogeneous varieties
  Canad. Math. Bull. 59 (2016), 824--833.
  Final preprint version (20 April 2016, 10 pages).

• Incompressibility of products
  Revised version (with removed ``geometrically split'' condition), 8 February 2015, 6 pages.
  (Not intended for a journal submission because contained in Incompressibility of products of pseudo-homogeneous varieties. )

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 547 (2015, Jan 31, 7 pages)
  is now obsolete.

• Incompressible Grassmannians of isotropic subspaces
  Bull. Soc. Math. France 144 (2016), no. 4, 763--773.
  Final preprint version (11 February 2016, 9 pages).

• Incompressibility of products by Grassmannians of isotropic subspaces
  Revised version, 1 February 2015, 12 pages.
  (Not intended for a journal submission because the main result has been covered by Incompressibility of products of pseudo-homogeneous varieties
  and the rest is contained in Incompressible Grassmannians of isotropic subspaces. )

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 541 (2014, Sep 23, 12 pages)
  is now obsolete.

• Unitary Grassmannians of division algebras
  Transform. Groups 21 (2016), no. 1, pp. 115--127.
  Final preprint version (31 December 2014, 12 pages).
  

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 539 (2014, August 22, 9 pages).
  is now obsolete.

• Incompressibility of products of Weil transfers of generalized Severi-Brauer varieties
  Math. Z. 279 (2015), no. 3-4, 767--777.
  Final preprint version.

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 536 (2014, June 26, 12 pages)
  is now obsolete.

• (with Z. Reichstein and with an appendix by J. Pevtsova and Z. Reichstein)
  A numerical invariant for linear representations of finite groups
  Comment. Math. Helv. 90 (2015), no. 3, 667–701.
  Final preprint version.

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 534 (extended version 2014, June 18, 24 pages)
  is now obsolete.

• (with A. S. Merkurjev)
  Motivic decomposition of compactifications of certain group varieties
  J. Reine Angew. Math. 745 (2018), 41--58.
  Final preprint version (26 Feb 2016, 18 pages).

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 528 (extended version 2014, Feb 22, 18 pages)
  is now obsolete.

• Minimal canonical dimensions of quadratic forms
  Documenta Math. Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday (2015), 367--385.
  Final preprint version (February 2014, 17 pages).

  The previous version
  Linear Algebraic Groups and Related Structures (preprint server) 509 (2013, Sep 1, revised 2013, Sep 13)
  is now obsolete.

• (with A. S. Merkurjev)
  Hermitian forms over quaternion algebras
  Compos. Math. 150 (2014), 2073--2094.
  Final preprint version (May 2014, 24 pages).

  The previous version
  Linear Algebraic Groups and Related Structures (preprint server) 498 (2013, May 13, 22 pages)
  is now obsolete.

• Incompressibility of generic torsors of norm tori
  Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 414 (2013), 106--112.
  Final preprint version (2013, Jan 25, 6 pages).
  

  The initial version
  Linear Algebraic Groups and Related Structures (preprint server) 475 (2012, Aug 8, 5 pages)
  is now obsolete.

• Orthogonal and symplectic grassmannians of division algebras
  J. Ramanujan Math. Soc. 28 (2013), no. 2, 213--222.
  Final preprint version (2012, Dec 3, 9 pages).

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 469 (2012, May 21, 8 pages)
  is obsolete.

• Sufficiently generic orthogonal grassmannians
  J. Algebra 372 (2012) 365--375.
  Final preprint version (2012, Oct 8, 13 pages).

• (with A. S. Merkurjev)
  On standard norm varieties
  Ann. Sci. Éc. Norm. Supér. (4) 46, fascicule 1 (2013), 175--214.
  Final preprint version (18 June 2012, 38 pages).

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 456 (2012, Jan 4, 37 pages)
  is obsolete.

• Unitary grassmannians
  J. Pure Appl. Algebra 216 (2012), no. 12, 2586--2600
  Final preprint version (15 Feb. 2012, 25 pages).

  Here is a corrected version of Example 9.12.

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 424 (2011, Mar 17, revised 2011, Oct 9, 22 pages)
  is obsolete.

• Variations on a theme of rationality of cycles
  Cent. Eur. J. Math. 11 (2013), no. 6, 1056--1067.
  Final preprint version (16 July 2012, 14 pages).

  The version Linear Algebraic Groups and Related Structures (preprint server) 443 (2011, Sep 21, 13 pages)
  is obsolete.

• Incompressibility of orthogonal grassmannians
  C. R. Math. Acad. Sci. Paris 349 (2011) 1131--1134.
  Final preprint version (July 2011, 5 pages): arXiv copy

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 437 (2011, Jun 30, 5 pages)
  is obsolete.

• (with M. Zhykhovich)
  Isotropy of unitary involutions
  Acta Math. 211 (2013), no. 2, 227--253.
  Final preprint version (4 June 2012, 22 pages).

  The version
  Linear Algebraic Groups and Related Structures (preprint server) 423 (2011, Mar 15, 20 pages)
  is obsolete.

• Incompressibility of generic orthogonal grassmannians
  Linear Algebraic Groups and Related Structures (preprint server) 409 (2010, Nov 23, 7 pages)

  (Not intended for a journal submission because contained in Sufficiently generic orthogonal grassmannians. )

• Hyperbolicity of unitary involutions
  Sci. China Math. 55 (2012), no. 5, 937--945.
  The original publication is available at www.scichina.com and www.springerlink.com
  Final preprint version.

  The version Linear Algebraic Groups and Related Structures (preprint server) 397 (2010, Jul 30, 10 pages)
  is obsolete.

• Codimension 2 cycles on quadratic Weil transfer of biquaternionic Severi-Brauer variety.
  Note, Jul 2010, 4 pages.

• Isotropy of symplectic involutions
  C. R. Math. Acad. Sci. Paris. 348 (2010), no. 21-22, 1151--1153.
  Final preprint version.

• Canonical dimension
  Proceedings of the ICM 2010, vol. II, 146--161.

• (with an appendix by J.-P. Tignol)
  Isotropy of orthogonal involutions
  Amer. J. Math. 135 (2013), 1--15.
  Final preprint version

  The preprint version
  Linear Algebraic Groups and Related Structures (preprint server) 371 (2009, Nov 21, 9 pages).
  is obsolete.

• Incompressibility of quadratic Weil transfer of generalized Severi-Brauer varieties
  J. Inst. Math. Jussieu 11 (2012), no. 01, 119-131.

• Upper motives of outer algebraic groups
  In Quadratic forms, linear algebraic groups, and cohomology, vol. 18 of Dev. Math. Springer, New York, 2010, pp. 249--258.
  Erratum

  The preprint version
  Linear Algebraic Groups and Related Structures (preprint server) 340 (2009, Jun 16, 7 pages)
  is obsolete

• Upper motives of algebraic groups and incompressibility of Severi-Brauer varieties
  J. Reine Angew. Math. 677 (2013), 179--198.
  Final preprint version.
  CAUTION: numbering of subsections in the journal version differs from the preprint.

  The preprint version
  Linear Algebraic Groups and Related Structures (preprint server) 333 (2009, Apr 3, revised: 2009, Apr 24, 18 pages)
  is obsolete.

  Here is A Simplification of Proof of Theorem 4.1

• with an Appendix by Jean-Pierre Tignol
  Hyperbolicity of orthogonal involutions
  Doc. Math. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010), 371--392.

  Final preprint version.

  The preprint version
  Linear Algebraic Groups and Related Structures (preprint server) 330 (2009, Mar 25, revised: 2009, Apr 24, 16 pages)
  is obsolete.

• Hyperbolicity of hermitian forms over biquaternion algebras
  (not intended for a journal submission because contained in Hyperbolicity of orthogonal involutions)
  Revised version (January 2009, 17 pages)
  Linear Algebraic Groups and Related Structures (preprint server) 316 (2008, Dec 16, revised: 2009, Jan 07), 17 p.

• (with R. Elman and A. Merkurjev)
  The Algebraic and Geometric Theory of Quadratic Forms
  pdf , dvi
  American Mathematical Society Colloquium Publications, 56.
  American Mathematical Society, Providence, RI, 2008. 435 pp.
  ISBN-10: 0-8218-4329-X, ISBN-13: 978-0-8218-4329-1.
  List of corrections

• On isotropy of quadratic pair
  Contemp. Math. 493 (2009), 211--218.
  Preprint version

• (with A. S. Merkurjev)
  Essential dimension of finite p-groups
  Invent. Math. 172, no. 3, 491--508 (2008).
  Final preprint version
  (the original publication is available at www.springerlink.com)

  The preprint version
  Essential dimension of finite groups
  Linear Algebraic Groups and Related Structures (preprint server) 263 (2007, Jun 25), 14 p.
  is obsolete.

• (with J.-L. Colliot-Thélène and A. Merkurjev)
  Rational surfaces and canonical dimension of PGL_6
  St. Petersburg Math. J. 19 (2008), no. 5, 793--804.
  Final preprint version.

  The preprint version
  Linear Algebraic Groups and Related Structures (preprint server) 231 (2006, Nov 25), 15 p.
  is now obsolete.

• Canonical dimension of (semi-)spinor groups of small ranks
  Pure Appl. Math. Q. 4 (2008), no. 4 (Jean-Pierre Serre special issue, part I), 1033--1039.

  An older version:
  Preprint of the Max-Planck-Institut für Mathematik MPIM2005-109 (December 2005), 5 pages.

• (with A. S. Merkurjev)
  Canonical p-dimension of algebraic groups
  Adv. Math. 205 (2006), 410--433.

  The preprint version
  Linear Algebraic Groups and Related Structures (preprint server) 170 (December 2004), 22 p.
  is now obsolete.

• A bound for canonical dimension of the (semi-)spinor groups
  Duke Math. J. 133 (2006), no. 2, 391--404.

  Revised preprint version.

  The preprint version
  A bound for canonical dimension of the spinor group,
  Linear Algebraic Groups and Related Structures (preprint server) 171 (December 2004), 10 p.
  is now obsolete.

• (with J. Hurrelbrink and U. Rehmann)
  The minimal height of quadratic forms of given dimension
  Arch. Math. (Basel) 87 (2006), no. 6, 522--529.

  Preprint version:
  Linear Algebraic Groups and Related Structures (preprint server) 157 (October 2004), 8 p.

• Canonical dimension of orthogonal groups
  (the pdf file has a wrong pagination)
  Transform. Groups 10 (2005), no. 2, 211--215.

  An obsolete preprint version:
  Linear Algebraic Groups and Related Structures (preprint server) 144 (July 2004), 4 p.

• A relation between higher Witt indices
  Revised version
  Proceedings of the St. Petersburg Mathematical Society. Vol. XI, 77--86,
  Amer. Math. Soc. Transl. Ser. 2, 218, Amer. Math. Soc., Providence, RI, 2006.

  An obsolete preprint version:
  Linear Algebraic Groups and Related Structures (preprint server) 141 (June 2004), 10 p.

• A descent of motivic isomorphisms
  Preprint, 2 p (not intended for a journal submission).

• Cycles on powers of quadrics
  Mathematisches Institut, Seminars 2003/04, Universitätsverlag Göttingen, (2004)

• Holes in I ⁿ.
  Ann. Sci. Ecole Norm. Sup. (4) 37 (2004), no. 6, 973--1002.

  An obsolete preprint version:
  Linear Algebraic Groups and Related Structures (preprint server) 128 (December 2003), 1-29.

• Third proof of second gap in dimensions of quadratic forms from I ⁿ.
  Proceedings of the International Conference on the Algebraic and Arithmetic Theory of Quadratic Forms,
  Dec. 11--18, 2002, Universidad de Talca, Chile.
  Contemp. Math. 344, 207--213.

  Preprint version:
  Prépublications de l'IHES M/03/08 (February 2003), 1-7.

• Izhboldin's results on stably birational equivalence of quadrics
  Springer Lect. Notes Math. 1835
  (Proceedings of the Summer School
  ``Geometric Methods in the Algebraic Theory of Quadratic Forms'', Lens, June 2000).
  Preprint version:
  Linear Algebraic Groups and Related Structures (preprint server) 96 (July 2002), 1--31.

• (with A. S. Merkurjev)
  Rost projectors and Steenrod operations
  Doc. Math. 7 (2002), 481--493.

• On the first Witt index of quadratic forms
  Invent. Math. 153 (2003), no. 2, 455-462.

  Preprint version (1 December 2002) ,

  An older version:
  Linear Algebraic Groups and Related Structures (preprint server) 91 (June 2002), 1-7.

• (with A. S. Merkurjev)
  Essential dimension of quadrics
  Invent. Math. 153 (2003), no. 2, 361-372.

  Preprint version (December 2002)

  An older version:
  Linear Algebraic Groups and Related Structures (preprint server) 90 (June 2002), 1-9.

• Motives and Chow groups of quadrics
  with application to the u-invariant
  (after Oleg Izhboldin)
  Springer Lect. Notes Math. 1835
  (Proceedings of the Summer School
  ``Geometric Methods in the Algebraic Theory of Quadratic Forms'', Lens, June 2000).
  Preprint version

• Characterization of minimal Pfister neighbors via Rost projectors .
  J. Pure Appl. Algebra 160 (2001), 195-227.
  Preprint version (September 1999), 1-33.

• On anisotropy of orthogonal involutions.
  J. Ramanujan Math. Soc. 15 (2000), no. 1, 1-22.
  Preprint version (October 1999), 1-15.

• Weil transfer of algebraic cycles
  Indag. Math. (N.S.) 11 (2000), no. 1, 73-86.
  Preprint version (August 18, 1999).

• Criteria of motivic equivalence for quadratic forms and central simple algebras
  Math. Ann. 317 (2000), no. 3, 585-611.
  Preprint version (October, 1999)

• Cohomology of relative cellular spaces and isotropic flag varieties
  St. Petersburg Math. J. 12 (2001), no. 1, 1-50.
  Preprint version.
  The russian version of this text
  (appeared in Algebra i Analiz 12 (2000), no. 1, 3-69).

• A shortened construction of the Rost motive
  Preprint (November, 1998), 1-4.
  This text is a modified version of:

  A direct construction of the Rost motive
  K-Theory Preprint Archives 282 (1998)

  and is dissolved in Characterization of minimal Pfister neighbors via Rost projectors (see above).

• (with Oleg Izhboldin)
  Generic splitting fields of central simple algebras: Galois cohomology and non-excellence
  Algebras and Representation Theory 2 (1999), no. 1, 19-59.
  Preprint version.

• (with Oleg Izhboldin)
  Some new examples in the theory of quadratic forms
  Math. Z. 234 (2000) 4, 647-695.

• Three theorems on common splitting fields of central simple algebras
  Israel J. Math. 111 (1999), 125-141.
  Preprint version.

• Cohomological Invariants of Homogeneous Varieties
  (with Applications to Quadratic Forms and Central Simple Algebras)
  Habilitationsschrift (1997), 1-172.

• (with Oleg Izhboldin)
  Isotropy of 8-dimensional quadratic forms over function fields of quadrics
  Comm. Algebra 27 (1999), no. 4, 1823--1841.

• (with Oleg Izhboldin)
  On the group H³(F(\psi,D)/F)
  Doc. Math. 2 (1997), 297-311.
  

• (with Anne Quéguiner)
  A criterion of decomposability for degree 4 algebras with unitary involution
  J. Pure Appl. Algebra 147 (2000), no. 3, 303-309.
  Preprint version.

• (with Oleg Izhboldin)
  Isotropy of 6-dimensional quadratic forms over function fields of quadrics
  J. Algebra 209 (1998), 65-93.
  Preprint version.

• (with Oleg Izhboldin)
  Isotropy of virtual Albert forms over function fields of quadrics
  Math. Nachr. 206 (1999), 111-122.

• Cycles de codimension 2 sur produits de variétés de Severi-Brauer
  Publ. Math. Fac. Sci. Besançon, Théorie des Nombres, Années 1994/95-1995/96, 1-15.

• Order of torsion in CH⁴ of quadrics
  Doc. Math. 1 (1996), 57-65.

• Codimension 2 cycles on Severi-Brauer varieties
  K-Theory 13 (1998), no. 4, 305-330.

• Torsion in CH² of Severi-Brauer varieties and indecomposability of generic algebras
  Manuscripta Math. 88 (1995), 109-117.
  Preprint version.

• On topological filtration for triquaternion algebra
  Nova J. Math. Game Theory Algebra 4 (1996), no. 2, 161-167.

• The Grothendieck Chow-motifs of Severi-Brauer varieties
  St. Petersbourg Math. J. 7 (1996), no. 4, 649-661.
  Preprint version.

• Chow groups of quadrics and index reduction formula
  Nova J. Algebra Geom. 3 (1995), no. 4, 357-379.

• On topological filtration for Severi-Brauer varieties II
  Amer. Math. Soc. Transl. 174 (1996), no. 2, 45-48.
  Preprint version.

• On topological filtration for Severi-Brauer varieties
  Proc. Symp. Pure Math. 58.2 (1995), 275-277.
  Preprint version.

• Chow groups of quadrics and the stabilization conjecture
  Adv. Soviet Math. 4 (1991), 3-8.

• Cycles of codimension 3 on a projective quadric
  J. Sov. Math. 63 (1993), no. 6, 678-682.

• The Grothendieck ring of quadrics, and gamma filtration. (Russian)
  Rings and modules. Limit theorems of probability theory, No. 3 (Russian),
  39–61, 256, Izd. St.-Peterbg. Univ., St. Petersburg, 1993.
  Preprint version (Russian, with a preliminary title)
  Abstract (Russian)
  A recommendation for publication (Russian)

• The Chow ring of a projective quadric (Russian)
  PhD Thesis, Leningrad, USSR, June 1990, 82 pages.

• (with A. S. Merkurjev) Chow groups of projective quadrics
  Leningrad (St. Petersburg) Math. J. 2 (1991), no. 3, 655-671.

• Algebro-geometric invariants of quadratic forms
  Leningrad (St. Petersburg) Math. J. 2 (1991), no. 1, 119-138.
  Russian original (Algebra i Analiz 2 (1990), vyp. 1).