*Algebraic K-Theory*

Masters course of the Section of mathematics

*Spring semester 2011*

Prof. Kathryn Hess Bellwald

SB-MATHGEOM

Assistant: Eric Finster

Contents

Schedule

Syllabus

Bibliography

Homework sets

Various files to download

Algebraic K-theory, which to any ring R associates a sequence of groups K_{0}R, K_{1}R, K_{2}R, etc., can be viewed as a theory of linear algebra
over an arbitrary ring.
We will study in detail the first three of these groups. The higher K-groups, as defined by Quillen, will be the subject of the course "Higher algebraic K-theory" in the fall semester of 2011.

Applications of algebraic K-theory to number theory, algebraic topology, algebraic geometry, representation theory and functional analysis will be sketched as well.

**Lectures: ** Fridays, 8:15 to 10:00

**Exercices:** Fridays, 10:15 to 12:00

**Room: **MA 12

I. Elementary category theory and module theory

II. K_{0} : Grothendieck groups, stability, tensor products, change of rings

III. K_{1} : elementary matrices, commutators and determinants

IV. K_{2}: Steinberg symbols, exact sequences, Matsumoto's theorem

Bruce A. Magurn, *An Algebraic Introduction to K-Theory,* Cambridge, 2002.

John Rognes, *Lecture Notes on Algebraic K-theory,* University of Oslo, 2010.

Jonathan Rosenberg, *Algebraic K-theory and its Applications,* Springer, 2004.

Charles Weibel, *The K-book: An Introduction to Algebraic K-theory,* (in progress).

(pdf files)

(pdf files)

Schedule of remaining lectures

Last update: 24.05.11