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Algebraic $$K$$-Theory
Edited by: A. A. Suslin
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1991; 170 pp; hardcover
Volume: 4
ISBN-10: 0-8218-4103-3
ISBN-13: 978-0-8218-4103-7
List Price: US$101 Member Price: US$80.80

This volume contains previously unpublished papers on algebraic $$K$$-theory written by Leningrad mathematicians over the last few years.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.
• N. A. Karpenko -- Chow groups of quadrics and the stabilization conjecture
• A. Nenashev -- Simplicial definition of $$\lambda$$-operations in higher $$K$$-theory
• I. A. Panin -- On algebraic $$K$$-theory of generalized flag fiber bundles and some of their twisted forms
• I. A. Panin -- On algebraic $$K$$-theory of some principal homogeneous spaces
• A. A. Suslin -- $$K$$-theory and $$\scr K$$-cohomology of certain group varieties
• A. A. Suslin -- $$SK_1$$ of division algebras and Galois cohomology
Part II: Milnor $$K$$-theory.
• 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. A. Suslin -- Triviality of the higher Chern classes in the $$K$$-theory of global fields
• A. A. Suslin and V. A. Yarosh -- Milnor's $$K_3$$ of a discrete valuation ring