Introduction to Algebraic K-Theory

✍ Scribed by John Milnor

• Publisher: Princeton University Press, University of Tokyo Press
• Year: 1971
• Tongue: English
• Leaves: 202
• Series: Annals of Mathematics Studies 72
• Category: Library

✦ Synopsis

Algebraic K-theory describes a branch of algebra that centers about two functors. K₀ and K₁, which assign to each associative ring ∧ an abelian group K₀Λ or K₁Λ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K₂, also from associative rings to abelian groups. Just as functors K₀ and K₁ are important to geometric topologists, K₂ is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

✦ Table of Contents

Cover
Title Page
Preface and Guide to the Literature
Contents
§1. Projective Modules and K₀Λ
§2. Constructing Projective Modules
§3. The Whitehead Group K₁Λ
§4. The Exact Sequence Associated with an Ideal
§5. Steinberg Groups and the Functor K₂
§6. Extending the Exact Sequences
§7. The Case of a Commutative Banach Algebra
§8. The Product K₁Λ ⊗ K₁Λ → K₂Λ
§9. Computations in the Steinberg Group
§10. Computation of K₂Z
§11. Matsumoto’s Computation of K₂ of a Field
§12. Proof of Matsumoto’s Theorem
§13. More about Dedekind Domains
§14. The Transfer Homomorphism
§15. Power Norm Residue Symbols
§16. Number Fields
Appendix — Continuous Steinberg Symbols
Index
Back Cover