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Yanchevskiĭ, Vyacheslav Ivanovich
academiсian of National Academy of Sciences of Ukraineacademiсian of National Academy of Sciences of Belarus
Professor
Doctor of physico-mathematical sciences (1981)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 9.07.1948
E-mail:
Keywords: linear algebraic groups, abelian varieties, Brauer groups of fields and schemes.
UDC: 512.552, 512.558, 512.7, 512.74, 512.75, 512.77, 513.6, 519.48, 523.015, 514.142
MSC: 14Hxx, 14Jxx, 14Kxx, 16H05, 16K20, 19Bxx, 20G15, 20G99, 16K20, 11E10, 11E04

Subject:

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).

Biography

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.

https://www.mathnet.ru/eng/person12250
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/215160
https://orcid.org/0000-0002-1868-5533

Publications in Math-Net.Ru Citations
2023
1. V. I. Yanchevskiĭ, A. S. Kondrat'ev, T. S. Busel, A. A. Osinovskaya, “To the memory of Irina Dmitrievna Suprunenko”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:1 (2023),  280–287  mathnet  mathscinet  elib
2022
2. V. I. Yanchevskiĭ, “Henselian division algebras and reduced unitary Whitehead groups for outer forms of anisotropic algebraic groups of the type $A_n$”, Mat. Sb., 213:8 (2022),  83–148  mathnet  mathscinet  zmath; Sb. Math., 213:8 (2022), 1096–1156  isi  scopus 2
2014
3. 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
2012
4. 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
2011
5. 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
6. 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
2009
7. 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 1
2008
8. 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 3
9. 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
2004
10. Dzmitry F. Bazyleu, Sergey V. Tikhonov, Vyacheslav I. Yanchevskii, “Conic bundles over real formal power series field”, Algebra Discrete Math., 2004, no. 1,  1–16  mathnet  mathscinet  zmath 2
2002
11. 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
1996
12. 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 4
1995
13. 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 5
14. 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 4
15. 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
1991
16. 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 4
17. 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 4
1990
18. I. L. Tomchin, V. I. Yanchevskii, “On the defect of valued skew-fields”, Dokl. Akad. Nauk SSSR, 314:5 (1990),  1082–1084  mathnet  mathscinet  zmath; Dokl. Math., 42:2 (1991), 612–614
19. 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
20. 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 7
21. 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
1989
22. 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 1
1987
23. 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 3
24. 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 3
1984
25. 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
26. 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 7
1979
27. 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 3
28. 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 6
29. 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 16
30. 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 2
1978
31. V. P. Platonov, V. I. Yanchevskii, “On stability in reduced $K$-theory”, Dokl. Akad. Nauk SSSR, 242:4 (1978),  769–772  mathnet  mathscinet  zmath 4
32. 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 12
1976
33. V. I. Yanchevskii, “Reduced unitary $K$-theory”, Dokl. Akad. Nauk SSSR, 229:6 (1976),  1332–1334  mathnet  mathscinet  zmath
34. 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 4
1975
35. 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 6
36. 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 5
37. V. P. Platonov, V. I. Yanchevskii, “On Harder's conjecture”, Dokl. Akad. Nauk SSSR, 221:4 (1975),  784–787  mathnet  zmath 6
1974
38. 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 15
1973
39. 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 8
2015
40. 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
2000
41. 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
1979
42. 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

Presentations in Math-Net.Ru
1. Henselian division algebras, $G$-involutions, and reduced unitary Whitehead groups for anisotropic outer forms of type $A_n$ (Zoom)
V. I. Yanchevskiĭ
“Numbers and functions” – Memorial conference for 80th birthday of Alexey Nikolaevich Parshin
November 28, 2022 13:10   
2. Henselian division algebras and reduced unitary Whitehead groups for outer forms of anisotropic algebraic groups of type $A_n$
V. I. Yanchevskii, S. V. Tikhonov
International Conference "Advances in Algebra and Applications"
June 23, 2022 10:00   

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