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Algebraic $K$-Theory
 
Edited by: A. A. Suslin
Front Cover for Algebraic $K$-Theory
Available Formats:
Hardcover ISBN: 978-0-8218-4103-7
Product Code: ADVSOV/4
List Price: $107.00
MAA Member Price: $96.30
AMS Member Price: $85.60
Electronic ISBN: 978-1-4704-4551-5
Product Code: ADVSOV/4.E
List Price: $107.00
MAA Member Price: $96.30
AMS Member Price: $85.60
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List Price: $160.50
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Front Cover for Algebraic $K$-Theory
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  • Front Cover for Algebraic $K$-Theory
  • Back Cover for Algebraic $K$-Theory
Algebraic $K$-Theory
Edited by: A. A. Suslin
Available Formats:
Hardcover ISBN:  978-0-8218-4103-7
Product Code:  ADVSOV/4
List Price: $107.00
MAA Member Price: $96.30
AMS Member Price: $85.60
Electronic ISBN:  978-1-4704-4551-5
Product Code:  ADVSOV/4.E
List Price: $107.00
MAA Member Price: $96.30
AMS Member Price: $85.60
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $160.50
MAA Member Price: $144.45
AMS Member Price: $128.40
  • Book Details
     
     
    Advances in Soviet Mathematics
    Volume: 41991; 170 pp
    MSC: Primary 11; 13; 14; 16; 18; 19;

    This volume contains previously unpublished papers on algebraic \(K\)-theory written by Leningrad mathematicians over the last few years.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 [ MR MR1124621 ]
    • N. Karpenko - Chow groups of quadrics and the stabilization conjecture
    • A. Nenashev - Simplicial definition of $\lambda $-operations in higher $K$-theory
    • I. Panin - On algebraic $K$-theory of generalized flag fiber bundles and some of their twisted forms
    • I. Panin - On algebraic $K$-theory of some principal homogeneous spaces
    • A. Suslin - $K$-theory and $\mathcal {K}$-cohomology of certain group varieties
    • A. Suslin - $SK_1$ of division algebras and Galois cohomology
    • Part II. Milnor $K$-theory [ MR MR1124621 ]
    • 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. Suslin - Triviality of the higher Chern classes in the $K$-theory of global fields
    • A. Suslin and V. Yarosh - Milnor’s $K_3$ of a discrete valuation ring
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Volume: 41991; 170 pp
MSC: Primary 11; 13; 14; 16; 18; 19;

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.

  • Part I. Computations in $K$-theory [ MR MR1124621 ]
  • N. Karpenko - Chow groups of quadrics and the stabilization conjecture
  • A. Nenashev - Simplicial definition of $\lambda $-operations in higher $K$-theory
  • I. Panin - On algebraic $K$-theory of generalized flag fiber bundles and some of their twisted forms
  • I. Panin - On algebraic $K$-theory of some principal homogeneous spaces
  • A. Suslin - $K$-theory and $\mathcal {K}$-cohomology of certain group varieties
  • A. Suslin - $SK_1$ of division algebras and Galois cohomology
  • Part II. Milnor $K$-theory [ MR MR1124621 ]
  • 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. Suslin - Triviality of the higher Chern classes in the $K$-theory of global fields
  • A. Suslin and V. Yarosh - Milnor’s $K_3$ of a discrete valuation ring
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