**Advances in Soviet Mathematics**

1991;
170 pp;
Hardcover

MSC: Primary 11; 13; 14; 16; 18; 19;
Secondary 55

**Print ISBN: 978-0-8218-4103-7
Product Code: ADVSOV/4**

List Price: $107.00

AMS Member Price: $85.60

MAA Member Price: $96.30

**Electronic ISBN: 978-1-4704-4551-5
Product Code: ADVSOV/4.E**

List Price: $107.00

AMS Member Price: $85.60

MAA Member Price: $96.30

# Algebraic \(K\)-Theory

Share this page *Edited by *
*A. A. Suslin*

This volume contains previously unpublished papers on algebraic \(K\)-theory written by Leningrad mathematicians over the last few years.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

## Algebraic $K$-Theory

- Cover Cover11
- Title page i2
- Contents iii4
- Preface v6
- Part I. Computations in πΎ-theory 18
- Chow groups of quadrics and the stabilization conjecture 310
- Simplicial definition of π-operations in higher πΎ-theory 916
- On algebraic πΎ-theory of generalized flag fiber bundles and some of their twisted forms 2128
- On algebraic πΎ-theory of some principal homogeneous spaces 4754
- πΎ-theory and π¦-cohomology of certain group varieties 5360
- ππΎβ of division algebras and Galois cohomology 7582
- Part II. Milnor πΎ-theory 101108
- On class field theory of multidimensional local fields of positive characteristic 103110
- On π-torsion in πΎ^{π}_{*} for fields of characteristic π 129136
- Triviality of the higher Chern classes in the πΎ-theory of global fields 145152
- Milnorβs πΎβ of a discrete valuation ring 155162
- Back Cover Back Cover1178