Lectures on Algebraic K-theory
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 firstname.lastname@example.org.
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