Publications
Mikhail Borovoi

  1. M. Borovoi, The first and second homotopy groups of a homogeneous space of a complex linear algebraic group, J. Lie Theory 33 (2023), no. 2, 687–700, arXiv.2207.08887 [math.AG].

  2. M. Borovoi, with an appendix by Z. Rosengarten, Criterion for surjectivity of localization in Galois cohomology of a reductive group over a number field, to appear in C. R. Math. Acad. Sci. Paris, arXiv:2209.02069 [math.NT], DOI: 10.5802/crmath.455.

  3. M. Borovoi and D. A. Timashev, Galois cohomology and component group of a real reductive group, to appear in Israel J. Math., arXiv:2110.13062 [math.GR], DOI: 10.1007/s11856-023-2526-4.

  4. M. Borovoi and O. Gabber, A short proof of Timashev's theorem on the real component group of a real reductive group, Arch. Math. (Basel) 120 (2023), no. 1, 9–13, arXiv:2204.11482 [math.GR], DOI: 10.1007/s00013-022-01798-y.

  5. M. Borovoi, Galois cohomology of reductive algebraic groups over the field of real numbers, Commun. Math. 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik), 191-201, arXiv:1401.5913 [math.GR], DOI: 10.46298/cm.9298.

  6. M. Borovoi and G. Gagliardi, Existence of equivariant models of spherical varieties and other G-varieties, Int. Math. Res. Not. IMRN 2022, no. 20, 15932-16034, arXiv:1810.08960 [math.AG], DOI: 10.1093/imrn/rnab102.

  7. L. Moser-Jauslin and R. Terpereau, with an appendix by M. Borovoi, Real structures on horospherical varieties, Michigan Math. J. 71 (2022), 283-320, arXiv:1808.10793[math.AG], DOI: 10.1307/mmj/20195793.

  8. M. Borovoi, W.A. de Graaf, and H.V. Lê, Classification of real trivectors in dimension nine, J. Algebra 603 (2022), 118–163, arXiv:2108.00790 [math.RT], DOI: 10.1016/j.jalgebra.2022.04.003.

  9. M. Borovoi, A. A. Gornitskii, and Z. Rosengarten, Galois cohomology of real quasi-connected reductive groups, Arch. Math. (Basel) 118 (2022), 27-38, arXiv:2103.04654 [math.RT], DOI: 10.1007/s00013-021-01678-x.

  10. M. Borovoi and D. A. Timashev, Galois cohomology of real semisimple groups via Kac labelings, Transform. Groups 26 (2021), 433-477, arXiv:2008.11763 [math.GR], DOI: 10.1007/S00031-021-09646-z.

  11. M. Borovoi, C. Daw, and J. Ren, Conjugation of semisimple subgroups over real number fields of bounded degree, Proc. Amer. Math. Soc. 149 (2021), no. 12, 4973–4984, arXiv:1802.05894[math.GR], DOI: 10.1090/proc/14505.

  12. M. Borovoi, N. Semenov, and M. Zhykhovich, Hasse principle for Rost motives, Int. Math. Res. Not. IMRN 2021, no. 6, 4231–4254, arXiv:1711.04356[math.AG], DOI: 10.1093/imrn/rny300.

  13. M. Borovoi, with an appendix by G. Gagliardi, Equivariant models of spherical varieties, Transform. Groups 25 (2020), 391-439, arXiv:1710.02471[math.AG], DOI:10.1007/S00031-019-09531-w.

  14. M. Borovoi and Z. Evenor, Real homogenous spaces, Galois cohomology, and Reeder puzzles,, J. Algebra 467 (2016), 307-365, arXiv:1406.4362 [math.GR], DOI: 10.1016/j.jalgebra.2016.07.032.

  15. M. Borovoi and Y. Cornulier, Conjugate complex homogeneous spaces with non-isomorphic fundamental groups, C. R. Acad. Sci. Paris, Ser I 353 (2015), 1001-1005, arXiv:1505.02323 [math.AG], DOI: 10.1016/j.crma.2015.09.010.

  16. M. Borovoi with an appendix by I. Dolgachev, Real reductive Cayley groups of rank 1 and 2, J. Algebra 436 (2015), 35-60, arXiv:1212.1065 [math.AG], DOI: 10.1016/j.jalgebra.2015.03.034.

  17. M. Borovoi and B. Kunyavskii, Stably Cayley semisimple groups, Documenta Math. Extra Volume: Alexander S. Merkurjev's Sixtieth Birthday (2015) 85-112, arXiv:1401.5774 [math.AG], online.

  18. M. Borovoi, Homogeneous spaces of Hilbert type, Int. J. Number Theory, 11 (2015), 397-405, arXiv:1304.1872 [math.NT], DOI: 10.1142/S1793042115500207.

  19. M. Borovoi and C.D. González-Avilés, The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme, Cent. Eur. J. Math. 12(4) (2014), 545-558, arXiv:1303.6586 [math.AG], DOI: 10.2478/s11533-013-0363-0.

  20. M. Borovoi, B. Kunyavskii, N. Lemire, and Z. Reichstein, Stably Cayley groups in characteristic zero, Int. Math. Res. Not. IMRN 2014, 5340-5397, arXiv:1207.1329 [math.AG], DOI: 10.1093/imrn/rnt123.

  21. M. Borovoi, On the unramified Brauer group of a homogeneous space, Algebra i Analiz 25:4 (2013), 23-27 (Russian), transl. in St. Petersburg Math. J. 25 (2014), 529-532, arXiv:1206.1023 [math.AG], online (Russian), English:DOI: 10.1090/S1061-0022-2014-01304-0.

  22. M. Borovoi, C. Demarche et D. Harari, Complexes de groupes de type multiplicatif et groupe de Brauer non ramifié des espaces homogènes, Ann. Sci. Éc. Norm. Supér. (4), 46 (2013), 651-692, arXiv:1203.5964[math.AG], DOI: 10.24033/asens.2198.

  23. M. Borovoi and C. Demarche, Manin obstruction to strong approximation for homogeneous spaces, Comment. Math. Helv. 88 (2013), 1-54, arXiv:0912.0408[math.NT], DOI: 10.4171/CMH/277.

  24. M. Borovoi and T.M. Schlank, A cohomological obstruction to weak approximation for homogeneous spaces, Moscow Math. J. 12 (2012), 1-20, arXiv:1012.1453[math.NT], online.

  25. M. Borovoi and J. van Hamel, Extended equivariant Picard complexes and homogeneous spaces, Transform. Groups 17 (2012), 51-86, arXiv:1010.3414[math.AG], DOI: 10.1007/s00031-011-9163-4.

  26. M. Borovoi, Vanishing of algebraic Brauer-Manin obstructions, J. Ramanujan Math. Soc. 26 (2011), 333-349, arXiv:1012.1189[math.NT].

  27. M. Borovoi, Symmetric homogeneous spaces with finitely many orbits, Appendix to the paper of A. Gorodnik and Hee Oh: Rational points on homogeneous varieties and equidistribution of adelic periods, Geom. Funct. Anal., 21 (2011), 319--392, arXiv:0803.1996[math.AG], DOI: 10.1007/s00039-011-0113-z.

  28. M. Borovoi and Z. Reichstein, Toric-friendly groups, Algebra Number Theory 5 (2011), 361-378, arXiv:1003.5894[math.AG], DOI: 10.2140/ant.2011.5.361.

  29. M. Borovoi, The defect of weak approximation for homogeneous spaces, II, Dal'nevost. Mat. Zh. 9 (2009), 15-23, arXiv:0804.4767 [math.NT], online.

  30. M. Borovoi and J. van Hamel, Extended Picard complexes and linear algebraic groups, J. Reine Angew. Math. 627 (2009), 53-82, arXiv:math/0612156, DOI: 10.1515/CRELLE.2009.011.

  31. M. Borovoi, J.-L. Colliot-Thélène and A.N. Skorobogatov, The elementary obstruction and homogeneous spaces, Duke Math. J. 141 (2008), 321-364, arXiv:math/0611700, DOI: 10.1215/S0012-7094-08-14124-9.

  32. M. Borovoi and J. van Hamel, Extended Picard complexes for algebraic groups and homogeneous spaces, C. R. Acad. Sci. Paris Ser I 342 (2006) 671-674, pdf, online.

  33. T. Bandman, M. Borovoi, F. Grunewald, B. Kunyavskii and E. Plotkin, Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups, Manuscr. Math. 119 (2006) 365-381, pdf, DOI: 10.1007/s00229-006-0627-0.

  34. M. Borovoi and B. Kunyavskii, with an appendix by P. Gille, Arithmetical birational invariants of linear algebraic groups over two-dimensional geometric fields, J. of Algebra 276 (2004) 292-339, pdf, DOI: 10.1016/j.jalgebra.2003.10.024.

  35. M. Borovoi, On representations of integers by indefinite ternary quadratic forms. J. of Number Theory 90 (2001), 281-293, pdf, DOI: 10.1006/jnth.2001.2662.

  36. M. Borovoi and B. Kunyavskii, Brauer equivalence in a homogeneous space with connected stabilizer. Michigan Math. J. 49 (2001), 197-205, pdf.

  37. M. Borovoi and B. Kunyavskii, Formulas for the unramified Brauer group of a principal homogeneous space of a linear algebraic group. J. Algebra 225 (2000), 804-821, pdf, DOI: 10.1006/jabr.1999.8153.

  38. M. Borovoi, The defect of weak approximation for homogeneous spaces. Ann. Fac. Sci. Toulouse 8 (1999), 219-233, pdf, online.

  39. M. Borovoi, A cohomological obstruction to the Hasse principle for homogeneous spaces. Math. Ann. 314 (1999), 491-504, pdf, DOI: 10.1007/s002080050304.

  40. M. Borovoi, Abelian Galois cohomology of reductive groups. Memoirs of the AMS 132 (1998), No. 626, 1-50, pdf, DOI: http://dx.doi.org/10.1090/memo/0626.

  41. M. Borovoi and B. Kunyavskii, Spherical spaces for which the Hasse principle and weak approximation fail. Collect. Math. 48 (1997), 41-52, ps.

  42. M. Borovoi, Abelianization of the first Galois cohomology of reductive groups. Internat. Math. Res. Not. 1996, 401-407, online.

  43. M. Borovoi, The Brauer-Manin obstruction to the Hasse principle for homogeneous spaces with connected or abelian stabilizer. J. reine angew. Math. 473 (1996), 181-194, pdf, DigiZeitschriften, DOI: 10.1515/crll.1995.473.181.

  44. M. Borovoi and Z. Rudnick, Hardy-Littlewood varieties and semisimple groups. Invent. Math. 119 (1995), 37-66, pdf, DigiZeitschriften, DOI: 10.1007/BF01245174.

  45. M. Borovoi, Abelianization of the second nonabelian Galois cohomology. Duke Math. J. 72 (1993), 217-239, DOI: 10.1215/S0012-7094-93-07209-2.

  46. M. Borovoi, The Hasse principle for homogeneous spaces. J. reine angew. Math. 426 (1992), 179-192.

  47. M. Borovoi, On weak approximation in homogeneous spaces of simply connected algebraic groups. Proceedings of Internat. Conf. "Automorphic Functions and Their Applications, Khabarovsk, June 27-July 4, 1988" (N. Kuznetsov, V. Bykovsky, eds.) Khabarovsk, 1990, 64-81, scan.

  48. M. Borovoi, On weak approximation in homogeneous spaces of algebraic groups. Soviet Math. Doklady 42 (1991), 247-251.

  49. M. Borovoi, On strong approximation for homogeneous spaces. Doklady Akad. Nauk BSSR 33 (1989), N4, 293-296 (Russian).

  50. M. Borovoi, The abstract simplicity of groups of type D_n over number fields. Russian Math. Surveys 43 (1988), N5, 213-214.

  51. M. Borovoi, Galois cohomology of real reductive groups, and real forms of simple Lie algebras. Functional. Anal. Appl. 22:2 (1988), 135-136, online: Russian, English, DOI: 10.1007/BF01077606.

  52. M. Borovoi, On the group of points of a semisimple group over a real closed field. Problems in Group Theory and Homological Algebra, Yaroslavl (1987), 142-149 (Russian); English translation: Selecta Math. Soviet. 9 (1990), 331-338.

  53. M. Borovoi, Conjugation of Shimura varieties. In:"Proc. Internat. Congr. Math., Berkeley, 1986", AMS, 1987, Vol. 1, pp. 783-790, online.

  54. M. Borovoi, Abstract simplicity of some simple anisotropic algebraic groups over number fields. Soviet Math. Doklady 32 (1985), N1, 191-193.

  55. M. Borovoi, Generators and relations in compact Lie groups. Functional. Anal. Appl. 18:2 (1984), 133-135, online: Russian, English, DOI: 10.1007/BF01077826.

  56. M. Borovoi, Langlands' conjecture concerning conjugation of connected Shimura varieties. Selecta Math. Soviet. 3 (1983-84), N1, 3-59.

  57. M. Borovoi, The conjecture of Langlands on conjugation of Shimura varieties. Functional. Anal. Appl. 16:4 (1982), 292-294, online: Russian, English.

  58. M. Borovoi, The Hodge group and endomorphism algebra of an Abelian variety. Problems in Group Theory and Homological Algebra, Yaroslavl (1981), 124-126, Russian, English.

  59. M. Borovoi, The Shimura-Deligne schemes M(G,h) and the rational cohomology classes of type (p,p) of Abelian varieties. Problems in Group Theory and Homological Algebra, vyp. 1, Yaroslavl (1977), 3-53 (Russian).

  60. M. Borovoi, The schemes M(G,h) and the Mumford-Tate group. Uspekhi Mat. Nauk 32 (1977), N6, 245-246 (Russian).

  61. M. Borovoi, On the action of the Galois group on rational cohomology classes of type (p,p) of Abelian varieties. Mat. Sbornik 94 (1974), N4, 649-652, Russian, English.

Preprints

  1. E. Vishnyakova, with an appendix by M. Borovoi, Automorphisms and real structures for a Π-symmetric super-Grassmannian, https://doi.org/10.48550/arXiv.2205.04380.

  2. M. Borovoi, W.A. de Graaf, and H.V. Lê, Real graded Lie algebras, Galois cohomology, and classification of trivectors in R9, arXiv:2106.00246 [math.RT].

  3. M. Borovoi, Extending the exact sequence of nonabelian H1, using nonabelian H2 with coefficients in crossed modules, arXiv:1608.07366 [math.GR].

  4. M. Borovoi, Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology. Preprint, 1992, pdf.

Last updated on December 6, 2023.

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