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Algebraic \(K\)-Theory
Edited by: A. A. Suslin

Advances in Soviet Mathematics
1991; 170 pp; hardcover
Volume: 4
ISBN-10: 0-8218-4103-3
ISBN-13: 978-0-8218-4103-7
List Price: US$107
Member Price: US$85.60
Order Code: ADVSOV/4
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This volume contains previously unpublished papers on algebraic \(K\)-theory written by Leningrad mathematicians over the last few years. The main topic of the first part is the computation of \(K\)-theory and \(K\)-cohomology for special varieties, such as group varieties and their principal homogeneous spaces, flag fiber bundles and their twisted forms, \(\lambda\)-operations in higher \(K\)-theory, and Chow groups of nonsingular quadrics. The second part deals with Milnor \(K\)-theory: Gersten's conjecture for \(K^M_3\) of a discrete valuation ring, the absence of \(p\)-torsion in \(K^M_*\) for fields of characteristic \(p\), Milnor \(K\)-theory and class field theory for multidimensional local fields, and the triviality of higher Chern classes for the \(K\)-theory of global fields.

Table of Contents

Part I: Computations in \(K\)-theory.
  • N. A. Karpenko -- Chow groups of quadrics and the stabilization conjecture
  • A. Nenashev -- Simplicial definition of \(\lambda\)-operations in higher \(K\)-theory
  • I. A. Panin -- On algebraic \(K\)-theory of generalized flag fiber bundles and some of their twisted forms
  • I. A. Panin -- On algebraic \(K\)-theory of some principal homogeneous spaces
  • A. A. Suslin -- \(K\)-theory and \(\scr K\)-cohomology of certain group varieties
  • A. A. Suslin -- \(SK_1\) of division algebras and Galois cohomology
Part II: Milnor \(K\)-theory.
  • I. Fesenko -- On class field theory of multidimensional local fields of positive characteristic
  • O. Izhboldin -- On \(p\)-torsion in \(K^M_*\) for fields of characteristic \(p\)
  • A. Musikhin and A. A. Suslin -- Triviality of the higher Chern classes in the \(K\)-theory of global fields
  • A. A. Suslin and V. A. Yarosh -- Milnor's \(K_3\) of a discrete valuation ring
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