This article is cited in 16 papers

Reduced unitary $K$-theory. Aplications to algebraic groups

V. I. Yanchevskii


Abstract: 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.

UDC: 513.6

MSC: Primary 18F25; Secondary 20G15, 14L10

Received: 22.03.1979

 English version: Mathematics of the USSR-Sbornik, 1981, 38:4, 533–548

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