Yanchevskii, Vyacheslav Ivanovich

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Total publications: 39
Scientific articles: 36

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Doctor of physico-mathematical sciences (1981)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 09.07.1948
Keywords: linear algebraic groups; abelian varieties; Brauer groups of fields and schemes.


The theory of Whitehead groups of spinor (jointly with A. P.Monastyrnyi) and unitary groups is developed. The reciprocity laws in Brauer groups of function fields of curves defined over number fields are described (jointly with V. I. Guletskii). The indicies of hyperelliptic curves defined over $p$-adic fields are computed (jointly with J. van Geel).


Graduated from the Mechanics and Mathematics Department of the Belarus State University in 1971 (the Higher Algebra Chair). Ph.D., 1974, the Institute of Mathematics, the National Academy of Sciences of Belarus. Doct. Sci., 1981, the same institute. More than 120 publications. I lead the research seminar at BSU on geometry. I and O. I. Tavgen lead the research seminar at BSU on algebra.

Vice-president of the Belarussian Mathematical Society.

Main publications:
  • Geel J., Yanchevskii V. I. Indices of huperelliptic curves over p-adic fields // Manuscripta Math. Springer-Verlag, 1998, V. 96, p. 317–333.
  • Guletskii V. I., Yanchevskii V. I. Reciprocity laws for simple algebras over function fields of number curves // Communications in Algebra, 2000, v. 28, no, 4, p. 1657–1683.
  • Rehmann U., Tikhonov S. V., Yanchevskii V. I. Two-torsion of the Brauer groups of hyperelliptic curves and unramified algebras over their function fields // Communications in Algebra, 2001, v. 29, no. 9, p. 3971–3988.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. S. V. Tikhonov, V. I. Yanchevskii, “Homomorphisms and involutions of unramified henselian division algebras”, Zap. Nauchn. Sem. POMI, 423 (2014),  264–275  mathnet  mathscinet; J. Math. Sci. (N. Y.), 209:4 (2015), 657–664  scopus
2. V. I. Yanchevskii, “Reduced Whitehead groups and conjugacy problem for special unitary groups of anisotropic hermitian forms”, Zap. Nauchn. Sem. POMI, 400 (2012),  222–245  mathnet  mathscinet; J. Math. Sci. (N. Y.), 192:2 (2013), 250–262  scopus
3. V. I. Yanchevskiĭ, “Homogeneous skew-fields of non-commutative rational functions and their reduced Whitehead groups”, Zap. Nauchn. Sem. POMI, 388 (2011),  270–308  mathnet; J. Math. Sci. (N. Y.), 183:5 (2012), 727–747  scopus
4. A. V. Prokopchuk, V. I. Yanchevskiĭ, “Invariant subalgebras of involutorial quaternion division algebras”, Zap. Nauchn. Sem. POMI, 388 (2011),  196–209  mathnet; J. Math. Sci. (N. Y.), 183:5 (2012), 685–691  scopus
5. A. V. Prokopchuk, V. I. Yanchevskii, “On another proof for B. Sury's theorem”, Zap. Nauchn. Sem. POMI, 365 (2009),  196–207  mathnet  zmath; J. Math. Sci. (N. Y.), 161:4 (2009), 565–571  scopus
6. U. Rehmann, S. V. Tikhonov, V. I. Yanchevskii, “Symbol algebras and cyclicity of algebras after a scalar extension”, Fundam. Prikl. Mat., 14:6 (2008),  193–209  mathnet  mathscinet; J. Math. Sci., 164:1 (2010), 131–142  scopus
7. S. V. Tikhonov, V. I. Yanchevskii, “Abelian crossed products and scalar extensions of central simple algebras”, Zap. Nauchn. Sem. POMI, 356 (2008),  179–188  mathnet  zmath; J. Math. Sci. (N. Y.), 156:6 (2009), 954–959  scopus
8. Dzmitry F. Bazyleu, Sergey V. Tikhonov, Vyacheslav I. Yanchevskii, “Conic bundles over real formal power series field”, Algebra Discrete Math., 2004, 1,  1–16  mathnet  mathscinet  zmath
9. S. V. Tikhonov, V. I. Yanchevskii, “The indices of central simple algebras over function fields of projective spaces over $P_{n,r}$-fields”, Mat. Sb., 193:11 (2002),  125–138  mathnet  mathscinet  zmath; Sb. Math., 193:11 (2002), 1691–1705  isi  scopus
10. V. I. Guletskii, V. I. Yanchevskii, “Ramification and reciprocity laws in Brauer groups of function fields of numerical curves of genus one”, Algebra i Analiz, 8:5 (1996),  210–228  mathnet  mathscinet  zmath; St. Petersburg Math. J., 8:5 (1997), 863–877
11. V. I. Yanchevskii, G. L. Margilin, “Brauer groups of local hyperelliptic curves with good reduction”, Algebra i Analiz, 7:6 (1995),  227–249  mathnet  mathscinet  zmath; St. Petersburg Math. J., 7:6 (1996), 1033–1048
12. V. I. Yanchevskii, G. L. Margilin, “Torsion and the Brauer groups of local elliptic curves”, Algebra i Analiz, 7:3 (1995),  200–239  mathnet  mathscinet  zmath; St. Petersburg Math. J., 7:3 (1996), 473–505
13. V. I. Yanchevskii, “The Hasse principle for Brauer groups of function fields on the products of Severi–Brauer varieties and projective quadrics”, Trudy Mat. Inst. Steklov., 208 (1995),  350–365  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 208 (1995), 309–322
14. I. L. Tomchin, V. I. Yanchevskii, “On defects of valued division algebras”, Algebra i Analiz, 3:3 (1991),  147–164  mathnet  mathscinet  zmath; St. Petersburg Math. J., 3:3 (1992), 631–647
15. V. P. Platonov, V. I. Yanchevskii, “Finite-dimensional skew fields”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 77 (1991),  144–262  mathnet  mathscinet  zmath
16. A. P. Monastyrnyi, V. I. Yanchevskii, “Whitehead groups of algebraic groups of classical type, and $R$-equivalence”, Dokl. Akad. Nauk SSSR, 314:1 (1990),  110–114  mathnet  mathscinet  zmath; Dokl. Math., 42:2 (1991), 351–355
17. A. P. Monastyrnyi, V. I. Yanchevskii, “Whitehead groups of spinor groups”, Izv. Akad. Nauk SSSR Ser. Mat., 54:1 (1990),  60–96  mathnet  mathscinet  zmath; Math. USSR-Izv., 36:1 (1991), 61–100
18. V. I. Yanchevskii, “Reduced norms of simple algebras over function fields”, Trudy Mat. Inst. Steklov., 183 (1990),  215–222  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 183 (1991), 261–269
19. A. P. Monastyrnyi, V. I. Yanchevskii, “On the Whitehead groups and the Kneser–Tits conjecture for spinor groups”, Dokl. Akad. Nauk SSSR, 307:1 (1989),  31–35  mathnet  mathscinet  zmath; Dokl. Math., 40:1 (1990), 23–27
20. V. P. Platonov, V. I. Yanchevskii, “Finite-dimensional Henselian division algebras”, Dokl. Akad. Nauk SSSR, 297:3 (1987),  542–547  mathnet  mathscinet; Dokl. Math., 36:3 (1988), 502–506
21. V. P. Platonov, V. I. Yanchevskii, “On the theory of Henselian division algebras”, Dokl. Akad. Nauk SSSR, 297:2 (1987),  294–298  mathnet  mathscinet  zmath; Dokl. Math., 36:3 (1988), 468–472
22. V. P. Platonov, V. I. Yanchevskii, “Dieudonné's conjecture on the structure of unitary groups, and division rings over Henselian fields”, Dokl. Akad. Nauk SSSR, 279:3 (1984),  546–549  mathnet  mathscinet  zmath
23. V. P. Platonov, V. I. Yanchevskii, “Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory”, Izv. Akad. Nauk SSSR Ser. Mat., 48:6 (1984),  1266–1294  mathnet  mathscinet  zmath; Math. USSR-Izv., 25:3 (1985), 573–599
24. V. P. Platonov, V. I. Yanchevskii, “$\mathrm{SK}_1$ for division rings of noncommutative rational functions”, Dokl. Akad. Nauk SSSR, 249:5 (1979),  1064–1068  mathnet  mathscinet  zmath
25. V. I. Yanchevskii, “A converse problem in reduced unitary $K$-theory”, Mat. Zametki, 26:3 (1979),  475–482  mathnet  mathscinet  zmath; Math. Notes, 26:3 (1979), 728–731  isi
26. V. I. Yanchevskii, “Reduced unitary $K$-theory. Aplications to algebraic groups”, Mat. Sb. (N.S.), 110(152):4(12) (1979),  579–596  mathnet  mathscinet  zmath; Math. USSR-Sb., 38:4 (1981), 533–548  isi
27. V. I. Yanchevskii, “Reduced unitary Whitehead groups of skew fields of noncommutative rational functions”, Zap. Nauchn. Sem. LOMI, 94 (1979),  142–148  mathnet  mathscinet  zmath; J. Soviet Math., 19:1 (1982), 1067–1071
28. V. P. Platonov, V. I. Yanchevskii, “On stability in reduced $K$-theory”, Dokl. Akad. Nauk SSSR, 242:4 (1978),  769–772  mathnet  mathscinet  zmath
29. V. I. Yanchevskii, “Reduced unitary $K$-theory and division rings over discretely valued Hensel fields”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978),  879–918  mathnet  mathscinet  zmath; Math. USSR-Izv., 13:1 (1979), 175–213  isi
30. V. I. Yanchevskii, “Reduced unitary $K$-theory”, Dokl. Akad. Nauk SSSR, 229:6 (1976),  1332–1334  mathnet  mathscinet  zmath
31. V. I. Yanchevskii, “Division rings over Hensel discretely valued fields and the Tannaka–Artin problem”, Dokl. Akad. Nauk SSSR, 226:2 (1976),  281–283  mathnet  mathscinet  zmath
32. V. P. Platonov, V. I. Yanchevskii, “On the Kneser–Tits conjecture for unitary groups”, Dokl. Akad. Nauk SSSR, 225:1 (1975),  48–51  mathnet  mathscinet  zmath
33. V. I. Yanchevskii, “The commutator subgroups of simple algebras with surjective reduced norms”, Dokl. Akad. Nauk SSSR, 221:5 (1975),  1056–1058  mathnet  mathscinet  zmath
34. V. P. Platonov, V. I. Yanchevskii, “On Harder's conjecture”, Dokl. Akad. Nauk SSSR, 221:4 (1975),  784–787  mathnet  zmath
35. V. I. Yanchevskii, “Simple algebras with involution, and unitary groups”, Mat. Sb. (N.S.), 93(135):3 (1974),  368–380  mathnet  mathscinet  zmath; Math. USSR-Sb., 22:3 (1974), 372–385
36. V. P. Platonov, V. I. Yanchevskii, “The structure of unitary groups and the commutator group of a simple algebra over global fields”, Dokl. Akad. Nauk SSSR, 208:3 (1973),  541–544  mathnet  mathscinet  zmath

37. V. I. Yanchevskii, D. G. Medvedev, A. E. Zalesskii, V. I. Sarvanov, “Dmitrii Alekseevich Suprunenko: on the 100th anniversary of his birth”, Tr. Inst. Mat., 23:2 (2015),  3–10  mathnet
38. S. I. Adian, E. I. Zel'manov, G. A. Margulis, S. P. Novikov, A. S. Rapinchuk, L. D. Faddeev, V. I. Yanchevskii, “Vladimir Petrovich Platonov (on his 60th birthday)”, Uspekhi Mat. Nauk, 55:3(333) (2000),  197–204  mathnet  mathscinet  zmath; Russian Math. Surveys, 55:3 (2000), 601–610  isi
39. V. P. Platonov, V. I. Yanchevskii, “Поправки к статье “О стабильности в приведенной $K$-теории” (ДАН, т. 242, № 4, 1978 г.)”, Dokl. Akad. Nauk SSSR, 245:3 (1979),  520  mathnet

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