An Introduction to K-theory
by Eric M. Friedlander
Number of pages: 78
The author's objective was to provide participants of the Algebraic K-theory Summer School an overview of various aspects of algebraic K-theory, with the intention of making these lectures accessible to participants with little or no prior knowledge of the subject.
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by Olivier Isely - EPFL
Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring A instead of over a field. Algebraic K-theory plays an important role in many subjects, especially number theory, algebraic topology and algebraic geometry.
by Charles Weibel - Rutgers
Algebraic K-theory is an important part of homological algebra. Contents: Projective Modules and Vector Bundles; The Grothendieck group K_0; K_1 and K_2 of a ring; Definitions of higher K-theory; The Fundamental Theorems of higher K-theory.
by Hyman Bass - Tata Institute of Fundamental Research
Topics: The exact sequence of algebraic K-theory; Categories of modules and their equivalences; The Brauer group of a commutative ring; The Brauer-Wall group of graded Azumaya algebras; The structure of the Clifford Functor.
by Jacek Brodzki - arXiv
An exposition of K-theory and cyclic cohomology. It begins with examples of various situations in which the K-functor of Grothendieck appears naturally, including the topological and algebraic K-theory, K-theory of C*-algebras, and K-homology.