Hardcover ISBN:  9780821841037 
Product Code:  ADVSOV/4 
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AMS Member Price:  $85.60 
Electronic ISBN:  9781470445515 
Product Code:  ADVSOV/4.E 
List Price:  $107.00 
MAA Member Price:  $96.30 
AMS Member Price:  $85.60 

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This volume contains previously unpublished papers on algebraic \(K\)theory written by Leningrad mathematicians over the last few years.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.

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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This volume contains previously unpublished papers on algebraic \(K\)theory written by Leningrad mathematicians over the last few years.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