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Algebraic $K$-Theory

Edited by: A. A. Suslin
Available Formats:
Hardcover ISBN: 978-0-8218-4103-7
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 MAA Member Price:$144.45
AMS Member Price: $128.40 Click above image for expanded view Algebraic$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

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This volume contains previously unpublished papers on algebraic $K$-theory written by Leningrad mathematicians over the last few years.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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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
Review Copy – for reviewers who would like to review an AMS book
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