01.01.06 (Mathematical logic, algebra, and number theory)
Birth date:
24.11.1973
E-mail:
,
Keywords:
abelian varieties; Brauer groups of fields and schemes
Subject:
The presentation of 2-torsion of Brauer groups of elliptic curves defined over complex formal power series by central simple algebras over function fields of curves is obtained. Jointly with U. Rehmann and V.I. Yanchevskii generators and relations in the 2-torsion part of the Brauer group of a hyperelliptic curve are found.
Biography
Graduated from the Mechanics and Mathematics Department of the Belarus State University in 1996 (the Higher Algebra Chair). Ph.D., 2000, the Institute of Mathematics, the National Academy of Sciences of Belarus. More than 10 publications.
Main publications:
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. Vol. 29, ¹ 9. P. 3971–3988.
N. A. Izobov, V. V. Gorokhovik, Yu. S. Kharin, L. A. Yanovich, D. F. Bazylev, V. V. Benyash-Krivets, I. D. Suprunenko, S. V. Tikhonov, “V. I . Yanchevskii is 70”, Algebra Discrete Math., 26:1 (2018), C–F
2016
2.
S. V. Tikhonov, “Division algebras of prime degree with infinite genus”, Trudy Mat. Inst. Steklova, 292 (2016), 264–267; Proc. Steklov Inst. Math., 292 (2016), 256–259
S. V. Tikhonov, V. I. Yanchevskii, “Homomorphisms and involutions of unramified henselian division algebras”, Zap. Nauchn. Sem. POMI, 423 (2014), 264–275; J. Math. Sci. (N. Y.), 209:4 (2015), 657–664
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; J. Math. Sci., 164:1 (2010), 131–142
S. V. Tikhonov, V. I. Yanchevskii, “Abelian crossed products and scalar extensions of central simple algebras”, Zap. Nauchn. Sem. POMI, 356 (2008), 179–188; J. Math. Sci. (N. Y.), 156:6 (2009), 954–959
2004
6.
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
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; Sb. Math., 193:11 (2002), 1691–1705
2018
8.
N. A. Izobov, V. V. Gorokhovik, Yu. S. Kharin, L. A. Yanovich, D. F. Bazylev, V. V. Benyash-Krivets, I. D. Suprunenko, S. V. Tikhonov, “Member of the National Academy of Sciences of Belarus V.I. Yanchevskii. Towards the 70th birthday”, Tr. Inst. Mat., 26:1 (2018), 6–8
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