Publications
Mikhail Borovoi

  1. M. Borovoi, Galois cohomology of reductive algebraic groups over the field of real numbers, to appear in Commun. Math. in the Special volume in memory of Arkady Onishchik, arXiv:1401.5913 [math.GR].

  2. M. Borovoi and G. Gagliardi, Existence of equivariant models of spherical varieties and other G-varieties, to appear in Int. Math. Res. Not. IMRN, arXiv:1810.08960 [math.AG], DOI: 10.1093/imrn/rnab102.

  3. L. Moser-Jauslin and R. Terpereau, with an appendix by M. Borovoi, Real structures on horospherical varieties, to appear in Michigan Math. J., arXiv:1808.10793[math.AG], DOI: 10.1307/mmj/20195793.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

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

  15. 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.

  16. 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.

  17. 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.

  18. 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.

  19. 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.

  20. 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.

  21. 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.

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

  23. 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.

  24. 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.

  25. 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.

  26. 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.

  27. 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.

  28. 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.

  29. 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.

  30. 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.

  31. 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.

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

  33. 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.

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

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

  36. 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.

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

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

  39. 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.

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

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

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

  43. 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.

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

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

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

  47. 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.

  48. 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.

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

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

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

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

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

  54. 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.

  55. 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).

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

  57. 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 and O. Gabber, A short proof of Timashev's theorem on the real component group of a real reductive group, https://doi.org/10.48550/arXiv.2204.11482.

  3. M. Borovoi and D.A. Timashev, Galois cohomology and component group of a real reductive group, arXiv:2110.13062 [math.GR].

  4. 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].

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

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


Last updated on February 27, 2022.

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