This book contains papers ranging over a number of topics relating to \(K\)-theory, including algebraic number theory, Grothendieck and Whitehead groups, group representation theory, linear algebraic groups, selfadjoint operator algebras, linear operators, homology and cohomology, and the use of \(K\)-theory in geometry.

Readership

Research mathematicians.

Table of Contents

• V. P. Platonov and A. A. Sharomet -- On the congruence problem for linear groups over arithmetic rings
• V. P. Platonov -- Birational properties of the reduced Whitehead group
• V. A. Artamonov -- Projective modules over group rings of nilpotent groups
• S. V. Vostokov and I. B. Fesenko -- On torsion in higher Milnor functors for multidimensional local fields
• A. A. Klyachko -- \(K\)-theory of Demazure models
• V. A. Lipnitskiĭ -- Norms in fields of real algebraic functions, and the reduced Whitehead group
• V. A. Lipnitskiĭ -- The reduced Whitehead group of weakly and totally ramified division algebras
• V. I. Kaskevich -- The structure of unitary and orthogonal groups over Henselian discretely normed Azumaya algebras
• V. I. Yanchevskiĭ -- Reduced unitary Whitehead groups and noncom-mutative rational functions
• I. I. Voronovich and V. I. Yanchevskiĭ -- Rational splitting fields of simple algebras, and unirationality of conic bundles
• V. V. Kursov and V. I. Yanchevskiĭ -- Crossed products of simple algebras and their automorphism groups
• A. S. Rapinchuk -- On the metaplectic kernel for anisotropic groups
• A. S. Rapinchuk -- The metaplectic kernel for the group \(SL(1,D)\)
• A. S. Rapinchuk -- On finite presentability of reduced norms in simple algebras
• A. Bovdi -- Unitarity of the multiplicative group of a group algebra
• O. I. Tavgen' -- Profinite completions of linear solvable groups
• O. I. Tavgen' -- On the Grothendieck and Platonov conjectures
• A. A. Sharomet -- The congruence problem for solvable algebraic groups over global fields of positive characteristic
• A. V. Prasolov -- \(K\)-theory of free products and the Bass problem
• A. V. Prasolov -- On a theorem of Gersten for graded rings
• A. V. Prasolov -- Algebraic \(K\)-theory of Banach algebras
• V. V. Benyash-Krivets -- On the finite generation of the character ring of three-dimensional unimodular group representations
• S. A. Baĭramov -- The \(K_G\)-functor on the category of inverse spectra of topological spaces
• M. R. Bunyatov and S. A. Baĭramov -- \(K\)-theory on the category of distributive lattices
• M. R. Bunyatov and S. A. Baĭramov -- \(K\)-theory on the category of topological spaces
• M. R. Bunyatov and S. A. Baĭramov -- \(K\)-theory on the category of Boolean algebras with closure
• M. R. Bunyatov and S. A. Baĭramov -- On index theory for a family of Fredholm complexes
• A. M. Bikchentaev -- On noncommutative function spaces
• A. V. Shtraus -- Generalized resolvents of nondensely defined bounded symmetric operators