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This article is cited in 12 scientific papers (total in 12 papers)
Reduced unitary $K$-theory and division rings over discretely valued Hensel fields
V. I. Yanchevskii
Abstract:
In this paper a Hermitian analog of reduced $K$-theory is constructed. The author studies the reduced unitary Whitehead groups $SUK_1(A)$ of simple finite-dimensional central algebras $A$ over a field $K$, which arise both in unitary $K$-theory and in the theory of algebraic groups. In the case of discretely valued Hensel fields $K$, with this end in mind groups of unitary projective conorms are introduced, with the aid of which the groups $SUK_1(A)$ are included in exact sequences whose terms are computable in many important cases. For a number of special fields $K$ of significant interest the triviality of the groups $SUK_1(A)$ is deduced from this. In addition, for an important class of simple algebras a formula is proved that reduces the computation of $SUK_1(A)$ to the calculation of so-called relative involutory Brauer groups, which are easily computable in many cases. Furthermore, for an arbitrary field $K$ the behavior of $SUK_1(A)$ is described when $K$ undergoes a purely transcendental extension, which in the case of division rings of odd index is a stability theorem important for many applications.
Bibliography: 31 titles.
Received: 21.07.1977
Citation:
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; Math. USSR-Izv., 13:1 (1979), 175–213
Linking options:
https://www.mathnet.ru/eng/im1851https://doi.org/10.1070/IM1979v013n01ABEH002018 https://www.mathnet.ru/eng/im/v42/i4/p879
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Abstract page: | 305 | Russian version PDF: | 95 | English version PDF: | 18 | References: | 53 | First page: | 1 |
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