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

Contents

Algebraic K-theory, which to any ring R associates a sequence of groups K₀R, K₁R, K₂R, 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.

Schedule

Lectures: Fridays, 8:15 to 10:00

Exercices: Fridays, 10:15 to 12:00

Room: MA 12
 

Syllabus

I. Elementary category theory and module theory
II. K₀ : Grothendieck groups, stability, tensor products, change of rings
III. K₁ : elementary matrices, commutators and determinants
IV. K₂: Steinberg symbols, exact sequences, Matsumoto's theorem