Lectures on Algebraic K-theory

J.F. Jardine

The pdf files below are my lecture notes for a course on Algebraic K-theory that I last gave at the University of Western Ontario in the Fall of 2014.

If you have comments or suggestions about these files, please contact me at jardine@uwo.ca.

Lecture 01: Some homotopy theory - a review

Lecture 02: Exact categories, Q-construction, Fundamental groupoid

Lecture 03:  Waldhausen's constructions, Additivity

Lecture 04:  The K-theory spectrum, Products

Lecture 05:  Group completion, Q=+ theorem, The defining acyclic map

Lecture 06:  Homotopy fibres, Resolution theorem, Dévissage

Lecture 07:  Abelian category localization, Coherent sheaves and open subschemes, Product formulas

Lecture 08:  K-theory with finite coefficients, Homology

Lecture 09:  K-theory of graded rings, Homotopy property

Lecture 10:  Rigidity

Lecture 11:  K-theory of finite fields