
Hardcover ISBN: | 978-0-8218-4103-7 |
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eBook ISBN: | 978-1-4704-4551-5 |
Product Code: | ADVSOV/4.E |
List Price: | $113.00 |
MAA Member Price: | $101.70 |
AMS Member Price: | $90.40 |
Hardcover ISBN: | 978-0-8218-4103-7 |
eBook: ISBN: | 978-1-4704-4551-5 |
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Hardcover ISBN: | 978-0-8218-4103-7 |
Product Code: | ADVSOV/4 |
List Price: | $113.00 |
MAA Member Price: | $101.70 |
AMS Member Price: | $90.40 |
eBook ISBN: | 978-1-4704-4551-5 |
Product Code: | ADVSOV/4.E |
List Price: | $113.00 |
MAA Member Price: | $101.70 |
AMS Member Price: | $90.40 |
Hardcover ISBN: | 978-0-8218-4103-7 |
eBook ISBN: | 978-1-4704-4551-5 |
Product Code: | ADVSOV/4.B |
List Price: | $226.00 $169.50 |
MAA Member Price: | $203.40 $152.55 |
AMS Member Price: | $180.80 $135.60 |
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Book DetailsAdvances in Soviet MathematicsVolume: 4; 1991; 170 ppMSC: 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This volume contains previously unpublished papers on algebraic \(K\)-theory written by Leningrad mathematicians over the last few years.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.
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Table of Contents
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Part I. Computations in $K$-theory [ MR MR1124621 ]
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N. Karpenko — Chow groups of quadrics and the stabilization conjecture
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A. Nenashev — Simplicial definition of $\lambda $-operations in higher $K$-theory
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I. Panin — On algebraic $K$-theory of generalized flag fiber bundles and some of their twisted forms
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I. Panin — On algebraic $K$-theory of some principal homogeneous spaces
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A. Suslin — $K$-theory and $\mathcal {K}$-cohomology of certain group varieties
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A. Suslin — $SK_1$ of division algebras and Galois cohomology
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Part II. Milnor $K$-theory [ MR MR1124621 ]
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I. Fesenko — On class field theory of multidimensional local fields of positive characteristic
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O. Izhboldin — On $p$-torsion in $K^M_*$ for fields of characteristic $p$
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A. Musikhin and A. Suslin — Triviality of the higher Chern classes in the $K$-theory of global fields
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A. Suslin and V. Yarosh — Milnor’s $K_3$ of a discrete valuation ring
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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.
-
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