This article is cited in 10 scientific papers (total in 10 papers)
Reduced unitary $K$-theory. Aplications to algebraic groups
V. I. Yanchevskii
In this paper a number of facts of reduced $K$-theory are proved, and some applications to algebraic groups are also considered.
In § 2 a stability theorem is proved for reduced unitary Whitehead groups under certain imbeddings in the skew field of fractions of noncommutative polynomial rings.
In §§ 3,4 the author considers reduced unitary Whitehead groups of skew fields over doubly henselian discretely valued fields; exact sequences are given for their computation. In particular, the nontriviality of the reduced unitary functor is proved for cyclic algebras.
The fifth and sixth sections are devoted to applications to algebraic groups. In particular, general problems of weak approximation and rationality for special unitary groups are solved in the negative.
Bibliography: 14 titles.
PDF file (1998 kB)
Mathematics of the USSR-Sbornik, 1981, 38:4, 533–548
MSC: Primary 18F25; Secondary 20G15, 14L10
V. I. Yanchevskii, “Reduced unitary $K$-theory. Aplications to algebraic groups”, Mat. Sb. (N.S.), 110(152):4(12) (1979), 579–596; Math. USSR-Sb., 38:4 (1981), 533–548
Citation in format AMSBIB
\paper Reduced unitary $K$-theory. Aplications to algebraic groups
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
V. P. Platonov, “The arithmetic theory of algebraic groups”, Russian Math. Surveys, 37:3 (1982), 1–62
Yu. L. Ershov, “Henselian valuations of division rings and the group $SK_1$”, Math. USSR-Sb., 45:1 (1983), 63–71
Zhuk I., “Rationality of Some Homogeneous Spaces of the So(Q) Group”, Dokl. Akad. Nauk Belarusi, 26:9 (1982), 773–775
V. P. Platonov, V. I. Yanchevskii, “Dieudonné's conjecture on the structure of unitary groups over a division ring, and Hermitian $K$-theory”, Math. USSR-Izv., 25:3 (1985), 573–599
Kaskevich V., “The Structure of Unitary and Orthogonal Groups Over Henselian Discrete Valuation Azymaya Algebras”, Dokl. Akad. Nauk Belarusi, 31:12 (1987), 1073–1076
A. P. Monastyrnyi, V. I. Yanchevskii, “Whitehead groups of spinor groups”, Math. USSR-Izv., 36:1 (1991), 61–100
Monastyrnyi A. Janchevskii V., “Whitehead-Groups of the Classical Type Algebraic-Groups and the R-Equivalence”, 314, no. 1, 1990, 110–114
Ulf Rehmann, Sergey V. Tikhonov, Vyacheslav I. Yanchevskiǐ, “Prescribed behavior of central simple algebras after scalar extension”, Journal of Algebra, 2011
V. I. Yanchevskii, “Reduced Whitehead groups and conjugacy problem for special unitary groups of anisotropic hermitian forms”, J. Math. Sci. (N. Y.), 192:2 (2013), 250–262
Wadsworth A.R., “Unitary Sk1 of Semiramified Graded and Valued Division Algebras”, Manuscr. Math., 139:3-4 (2012), 343–389
|Number of views:|