National Academy of Sciences of Belarus

YANCHEVSKY Vyacheslav Ivanovich

YANCHEVSKY Vyacheslav Ivanovich

Vyacheslav Ivanovich Yanchevsky (b. 09.07.1948, Minsk), mathematician. Academician of the National Academy of Sciences of Belarus (2014; corresponding member since 2009), Doctor of Physico-Mathematical Sciences (1981), Professor (1990).

Scientific works in the field of algebra, algebraic geometry and algebraic K-theory. He proposed a unified approach to solving problems of studying the structural properties of linear algebraic groups of the classical type. He constructed unitary and spinoric reduced K-theories to compute reduced Whitehead groups of Henselian finite-dimensional division algebras. He developed methods for describing special normal subgroups of multiplicative groups of algebras with involutions. Investigated the existence of cyclic involutions in classical division algebras. He developed methods for studying graded algebras with involutions, which made it possible to propose a uniform scheme for describing Whitehead groups of Henkel bodies and bodies of noncommutative rational functions. He established and proved reciprocity laws for the Brauer groups of function fields of curves over numeric fields. Solved the problem of the nontriviality of the anisotropic Whitehead unitary groups of division algebras with unitary involutions. Developed new methods for studying groups of rational points of linear algebraic groups based on establishing deep connections of the multiplicative structure of Azumaya algebras of geometric fields and their cohomological properties, which resulted in solving a number of problems in the theory of linear algebraic groups at the junction of algebraic K-theory and algebraic geometry.

Author of more than 200 scientific papers, incl. 2 textbooks for university math specialties.

Prize of the NAS of Belarus in 2008 for studying the structural properties of algebraic varieties.

Major papers:

  1. Янчевский В.И. Приведенная унитарная K-теория и тела над гензелевыми дискретно-нормированными полями. //Изв. АН СССР. Сер. мат. 1978. № 4. С. 879–918.
  2. Монастырный А.П., Янчевский В.И. Группы Уайтхеда спинорных групп //Изв. АН СССР. Сер. мат. 1990. Т. 54, № 1. С.60–96.
  3. Yanchevskii V.I. Symmetric and skew-symmetric elements of involutions, associated groups, and the problem of decomposability of involutions // Proceedings of Symposia in Pure Mathematics. Vol. 58.2. P. 431–444.