Publications

(DOI = link to a published version, PRP = link to an old preprint version)

ArXiv preprints / Notes

  1. Xiong, R., Zainoulline, K., Motivic Lefschetz theorem for twisted Milnor hypersurfaces, Preprint 2024, 10pp. (PRP)
  2. Xiong, R., Zainoulline, K., Zhong, C. On the formal Peterson subalgebra and its dual, Preprint 2023, 18pp. (PRP)
  3. Richmond, E., Zainoulline, K. Nil-Hecke rings and the Schubert calculus, Preprint 2023, 51pp. (PRP)
  4. Lanini, M., Xiong, R., Zainoulline, K. Structure algebras, Hopf-algebroids and oriented cohomology of a group, Preprint 2023, 27pp. (PRP)
  5. Fink, E., Zainoulline, K. Uniquely labelled geodesics of Coxeter groups. Preprint 2017, 23pp. (PRP)
  6. Zainoulline, K. On formal Schubert polynomials. Preprint 2014, 8pp.  (PRP)
  7. Zainoulline, K. Motivic decomposition of a generalized Severi-Brauer variety. (2006) 20pp.   (PRP)
  8. Gille, S.; Petrov, V.; Semenov, N.; Zainoulline, K. Introduction to motives and algebraic cycles on projective homogeneous varieties. (*.pdf)

Publications in refereed journals:

  1. Lenart, C., Su, C., Zainoulline, K., Zhong, C. Geometric properties of the Kazhdan-Lusztig Schubert basis. Algebra & Number Theory 17 (2023), no.2, 435-464. (DOI) (PRP)
  2. Gandhi, R., Savage, A., Zainoulline, K. Diagrammatics for F4. Bull. London Math. Soc. 55 (2023), no.1, 349-374. (DOI) (PRP)
  3. Zainoulline K. The canonical dimension of a semisimple group and the unimodular degree of a root system. Intern. Math. Res. Notices (2023), no.4, 2834-2845. (DOI) (PRP)
  4. Zainoulline, K. Localized operations on T-equivariant oriented cohomology of projective homogeneous varieties, J. Pure Appl. Algebra 226 (2022), Issue 3, 17pp. (DOI) (PRP)
  5. Lanini, M., Zainoulline, K. A Riemann-Roch type theorem for twisted fibrations of moment graphs. Arkiv för Matematik 59 (2021), no.2, 359-384. (DOI) (PRP)
  6. Lanini, M., Zainoulline, K. Twisted quadratic foldings of root systems. St.Petersburg Math. J. 33 (2022), no.1, 65-84. (DOI)  (PRP)
  7. Calmes, B., Neshitov, A., Zainoulline, K. Relative equivariant motives versus modules. Canadian Journal of Math. 73 (2021), Issue 1, 131-159.   (DOI) (PRP)
  8. Calmes, B., Zainoulline, K., Zhong, C. Formal affine Demazure and Hecke algebras of Kac-Moody root systems. Algebras and Representation Theory 23 (2020), 1031-1050.    (DOI) (PRP)
  9. Lenart, C., Zainoulline, K., Zhong, C. Parabolic Kazhdan-Lusztig basis, Schubert classes and equivariant oriented cohomology. J. Inst. Math. Jussieu 19 (2020), Issue 6, 1889-1929.   (DOI) (PRP)
  10. Devyatov, R., Lanini, M., Zainoulline, K. Oriented cohomology sheaves on double moment graphs. Documenta Math.  24 (2019), 563-608.   (DOI) (PRP)
  11. Calmes, B., Zainoulline, K., Zhong, C. Push-pull operators on the formal affine Demazure algebra and its dual. Manuscripta Math. 160 (2019), Issue 1-2, 9-50.   (DOI) (PRP)
  12. Neshitov, A., Petrov, V., Semenov, N., Zainoulline, K. Motivic decompositions of twisted flag varieties and representations of Hecke-type algebras. Advances in Math. 340 (2018), 791-818.   (DOI) (PRP)
  13. Baek, S., Devyatov, R., Zainoulline, K. The K-theory of versal flags and cohomological invariants of degree 3. Documenta Math. 22 (2017), 1117-1148.   (DOI)
  14. Lenart, C., Zainoulline, K. A Schubert basis in equivariant elliptic cohomology. New-York J. of Math. 23 (2017), 711-737.   (DOI) (PRP)
  15. Lenart, C., Zainoulline, K. Towards generalized cohomology Schubert calculus via formal root polynomials. Math. Research Letters 24, No. 3, (2017), 839-877.   (DOI)  (PRP)
  16. Calmes, B., Zainoulline, K., Zhong, C. A coproduct structure on the formal affine Demazure algebra. Math. Zeitschrift 282 (2016), no.3, 1191-1218. (DOI) (PRP)
  17. Calmes, B.; Zainoulline, K.; Zhong, C. Equivariant oriented cohomology of flag varieties. Documenta Math. Extra Volume: Alexander S. Merkurjev’s Sixtieth Birthday (2015), 113-144.    (DOI) (PRP)
  18. Merkurjev, A., Neshitov, A., Zainoulline, K. Cohomological Invariants in degree 3 and torsion in the Chow group of a versal flag. Compositio Math. 151, Issue 8, (2015), 1416-1432.    (DOI) (PRP)
  19. Malagon-Lopez, J.; Zainoulline, K.; Zhong, C. Invariants, exponents and formal group laws. J. of Algebra 409, July 1, (2014), 244-264.  (DOI)  (PRP)
  20. Hoffnung, A., Malagon-Lopez, J., Savage, A., Zainoulline, K. Formal Hecke algebras and algebraic oriented cohomology theories.  Selecta Math. 20 (2014), no.4, 1213-1245. (DOI) (PRP)
  21. Garibaldi, S.; Zainoulline, K. The gamma-filtration and the Rost invariant. J. Reine und Angew. Math. 696 (2014), 225-244. (DOI) (PRP)
  22. Baek, S., Zainoulline, K., Zhong, C. On the torsion of Chow groups of twisted Spin-flags. Math. Research Letters 20 (2013), no.4, 601-614. (DOI) (PRP)
  23. Ananyevskiy, A., Auel, A., Garibaldi, S., Zainoulline, K.  Exceptional collections of line bundles on projective homogeneous varieties. Advances in Math. 236 (2013) 111-130. (DOI)  (PRP)
  24. Calmes, B.; Petrov, V.; Zainoulline, K. Invariants, torsion indices and cohomology of complete flags. Ann. Sci. Ecole Norm. Sup. (4) 46 (2013), no.3, 405-448. (DOI) (PRP)
  25. Queguiner-Mathieu A.; Semenov, N.; Zainoulline, K. The J-invariant, Tits algebras and Triality. J. of Pure and Applied Algebra 216 (2012), 2614-2628. (DOI)  (PRP)
  26. Gille, S.; Zainoulline, K. Equivariant pretheories and invariants of torsors.  Transf. Groups 17 (2012), no.2, 471-498. (DOI) (PRP)
  27. Zainoulline, K. Twisted gamma-filtration of a linear algebraic group. Compositio Math. 148 (2012), no.5, 1645-1654. (DOI) (PRP)
  28. Baek, S.; Neher, E.; Zainoulline, K. Basic polynomial invariants, fundamental representations and the Chern class map. Documenta Math. 17 (2012), 135-150. (DOI) (PRP)
  29. Zainoulline, K. Degree formula for connective K-theory. Invent. Math. 179 (2010), no.3, 507-522. (DOI) (PRP)
  30. Semenov, N.; Zainoulline, K. Essential dimension of Hermitian spaces. Math. Annalen 346 (2010), no.2, 499-503. (DOI) (PRP)
  31. Panin, I.; Zainoulline, K. Gersten resolution with support. Manuscripta Math. 128 (2009), no. 4, 443-452. (DOI) (PRP)
  32. Zainoulline, K. Special correspondences and Chow traces of Landweber-Novikov operations. J. Reine und Angew. Math. 628 (2009), 195-204. (DOI) (PRP)
  33. Nikolenko, S.; Semenov, N.; Zainoulline, K. Motivic decompositions of anisotropic varieties of type F4 into generalized Rost motives. J. of K-theory 3 (2009), no.1, 85-102. (DOI) (PRP)
  34. Petrov, V.; Semenov, N.; Zainoulline, K. J-invariant of linear algebraic groups. Ann. Sci. Ecole Norm. Sup. (4) 41 (2008), no.6, 1023-1053. (DOI) (PRP)
  35. Vishik, A.; Zainoulline, K. Motivic Splitting Lemma. Documenta Math. 13 (2008), 81-96. (DOI) (PRP)
  36. Petrov, V.; Semenov, N.; Zainoulline, K. Zero-cycles on a twisted Cayley plane. Canadian Math. Bull. 51 (2008), no.1, 114-124. (DOI) (PRP)
  37. Zainoulline, K. Canonical p-dimensions of algebraic groups and degrees of basic polynomial invariants. London Math. Bull. 39 (2007), 301-304. (DOI) (PRP)
  38. Calmes, B.; Petrov, V.; Semenov, N.; Zainoulline, K. Chow motives of twisted flag varieties. Compositio Math. 142 (2006), no.4, 1063-1080. (DOI) (PRP)
  39. Semenov, N.; Zainoulline, K. A classification of projective homogeneous varieties up to motivic isomorphism (English. Russian original). J. Math. Sciences 140 (2007), no.5, 692-698; transl. Zap. Nauchn. Semin. POMI 330 (2006), 158-172. (DOI) (PRP)
  40. Nenashev, A.; Zainoulline, K. Oriented cohomology and motivic decompositions of relative cellular spaces. J. of Pure and Applied Algebra 205 (2006), no.2, 323-340. (DOI) (PRP)
  41. Zainoulline, K. On Knebusch’s Norm Principle for quadratic forms over semi-local rings. Math. Zeitschrift 251 (2005), no.2, 415-425. (DOI) (PRP)
  42. Ojanguren, M.; Panin, I.; Zainoulline, K. On the norm principle for quadratic forms. J. Ramanujan Math. Soc. 19 (2004), no.4, 1-12. (DOI) (PRP)
  43. Panin, I.; Zainoulline, K. Variations on the Bloch-Ogus Theorem. Documenta Math. 8 (2003), 51-67. (DOI) (PRP)
  44. Schmidt, A.; Zainoulline, K. Generic injectivity for etale cohomology and pretheories. J. of Algebra 263 (2003), no.2, 215-227. (DOI) (PRP)
  45. Zainoulline, K. The Purity Theorem for functors with transfers. K-Theory J. 22 (2001), no.4, 303-333. (DOI) (PRP)
  46. Zainullin, K. On Grothendieck’s conjecture about principal homogeneous spaces for some classical algebraic groups. (English. Russian original) St. Petersburg Math. J. 12 (2001), no.1, 117-143; translation from Algebra i Analiz 12(2000), no.1, 150-184. (DOI) (PRP)

Publications in refereed conference proceedings:

  1. Lenart, C., Zainoulline, K. Schubert Calculus in elliptic cohomology, Proc. of Conference on Formal Power Series and Algebraic Combinatorics, Discrete Math and Theoretical Computer Science, 2015, 757-768.
  2. Zainoulline, K. Witt group of a variety and the purity problem. Proceedings of conf. “Quadratic forms, linear algebraic groups, and cohomology”, Hyderabad 2009; Developments in Math. Vol. 18, Springer, 2010.   (*.pdf)
  3. Zainoulline, K. Non-hyperbolicity of orthogonal involutions. Appendix to the paper “Orthogonal involutions on algebras of degree 16 and the Killing form of E8” by Skip Garibaldi; Quadratic forms – algebra, arithmetic, and geometry, 159-160, Contemp. Math. 493, Amer. Math. Soc., Providence, RI, 2009.  (PRP)

Abstracts and technical reports:

  1. Zainoulline, K. The K-theory of versal flags and cohomological invariants of semisimple linear algebraic groups, Conf. on Algebraic groups, Oberwolfach 2017; Oberwolfach Reports, Vol. 21, 2017, pp. 1306-1307.
  2. Zainoulline, K. Motives of twisted flag varieties and Representations of Hecke-type algebras, Conf. on Algebraic cobordism and Projective homogeneous varieties, Oberwolfach 2016; Oberwolfach Reports, Vol. 13, Issue 1, 2016, pp. 215-265.
  3. Zainoulline, K. Formal group laws, Hecke algebras and algebraic oriented cohomology theories, Conf. on Algebraic groups, Oberwolfach 2013; Oberwolfach Reports, Vol. 10, Issue 2, 2013, pp. 963-1913.
  4. Zainoulline, K. The gamma filtration on projective homogeneous varieties. Joint Mathematics Meetings AMS Special Session on Linear Algebraic Groups: Their Arithmetic, Geometry, and Representations (04-07.01.2012), Boston, USA
  5. Zainoulline, K. Torsion in Chow groups of codimension 2 cycles for homogeneous varieties. Conf. on Motives and Homotopy Theory of Schemes, Oberwolfach 2010; Oberwolfach Reports, Vol. 7, Issue 2, 2010, pp. 955-1690.
  6. Zainoulline, K. Invariants, torsion indices and oriented cohomology of complete flags. Conf. on Quadratic forms and linear algebraic groups, Oberwolfach 2009; Oberwolfach Reports, Vol. 6, Issue 2, 2009, pp. 1419-1420.
  7. Zainoulline, K. Motivic decompositions of projective homogeneous varieties. Conf. on Quadratic Forms and Linear Algebraic Groups, Oberwolfach 2006; Oberwolfach reports, Vol. 3, Issue 3, 2006, pp. 1743-1794.;
  8. Zainoulline, K. On the norm principle for quadratic forms. Tschinkel, Yuri (ed.), Mathematisches Institut, Georg-August-Universitat Gottingen: Seminars (2004), 61-64.
  9. Zainullin, K.V. On central extensions of the group $\mathrm{SL}(D_N)$. (Russian) Gromov, N. A. (ed.), Algebra, differential equations and probability theory. Tr. Komi Nauchn. Tsentra UrO Ross. AN. 151, 44-50 (1997).