Publications
Mikhail Borovoi

  1. 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).

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

  3. M. Borovoi, The Shimura-Deligne schemes M(G,h) and the rational cohomology classes of type (p,p) of Abelian varieties. Voprosy Teorii Group i Gomologicheskoi Algebry, vyp. 1, Yaroslavl (1977), 3-53 (Russian).

  4. M. Borovoi, The Hodge group and the endomorphism algebra of an Abelian variety. Voprosy Teorii Grupp i Gomologicheskoi Algebry, Yaroslavl (1981), 124-126 (Russian).

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

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

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

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

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

  10. M. Borovoi, On the group of points of a semisimple group over a real closed field. Voprosy Teorii Grupp i Gomologicheskoi Algebry, Yaroslavl (1987), 142-149 (Russian); English translation: Selecta Math. Soviet. 9 (1990), 331-338.

  11. 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.

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

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

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

  15. 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.

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

  17. M. Borovoi, Abelianization of the second nonabelian Galois cohomology. Duke Math. J. 72 (1993), 217-239, online.

  18. M. Borovoi, Z. Rudnick, Hardy-Littlewood varieties and semisimple groups. Invent. Math. 119 (1995), 37-66, pdf, online.

  19. 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, online.

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

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

  22. M. Borovoi, Abelian Galois cohomology of reductive groups. Memoirs of the AMS 132 (1998), No. 626, 1-50, pdf.

  23. M. Borovoi, A cohomological obstruction to the Hasse principle for homogeneous spaces. Math. Ann. 314 (1999), 491-504, pdf, online.

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

  25. 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, online.

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

  27. M. Borovoi, On representations of integers by indefinite ternary quadratic forms. J. of Number Theory 90 (2001), 281-293, pdf, online.

  28. 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, 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, online.

  30. 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.

  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/0611700v2, online.

  32. M. Borovoi and J. van Hamel, Extended Picard complexes and linear algebraic groups, J. reine angew. Math. 627 (2009), 53-82, arXiv:math/0612156v1, online.

  33. M. Borovoi, The defect of weak approximation for homogeneous spaces, II, Dal'nevost. Mat. Zh. 9 (2009), 15-23, arXiv:0804.4767v2 [math.NT], online.

  34. M. Borovoi and C. Demarche, Manin obstruction to strong approximation for homogeneous spaces, to appear in Comment. Math. Helv., arXiv:0912.0408v2[math.NT].

  35. M. Borovoi and Z. Reichstein, Toric-friendly groups, Algebra and Number Theory 5 (2011), 361-378, arXiv:1003.5894v4[math.AG], online.

  36. 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, Geometric and Functional Analysis, 21 (2011), 319--392, arXiv:0803.1996v2[math.AG], online.

  37. M. Borovoi, Vanishing of algebraic Brauer-Manin obstructions, J. Ramanujan Math. Soc. 26 (2011), 333-349, arXiv:1012.1189v4[math.NT].

  38. M. Borovoi and J. van Hamel, Extended equivariant Picard complexes and homogeneous spaces, to appear in Transformation Groups, arXiv:1010.3414v2[math.AG], online.

  39. M. Borovoi and T.M. Schlank, A cohomological obstruction to weak approximation for homogeneous spaces, To appear in Moscow Math. J., arXiv:1012.1453v2[math.NT].

Preprints

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

  2. M. Borovoi, The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme, Appendix to the preprint of Cristian D. González-Avilés Abelian class groups of reductive group schemes, arXiv:1108.3264v2 [math.NT].

Last updated on November 1, 2011.