SoSe 20: Algebraic K-theory

Lectures: Wednesday 08-10 M104, Friday 08-10 M103
Exercises: Friday 10-12 M102

Algebraic K-theory was invented by Grothendieck in the 1950s in his proof of the Grothendieck–Riemann–Roch theorem. Nowadays algebraic K-theory plays an important role in various fields of mathematics, notably algebraic number theory, algebraic geometry, homotopy theory, and geometric topology. In particular it appears in the formulation of many deep conjectures. In this course, we will introduce algebraic K-theory in its various forms (K-theory of rings, of schemes, of exact categories, of Waldhausen categories) and prove some of the fundamental theorems of Quillen, Suslin, Waldhausen, etc.


Lecture notes


A good introductory reference is: For the state of the art in K-theory (in 2004), see: Some historical references in chronological order: