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


Bibliography


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).


Homework sets

(pdf files)

Exercise set 1

Exercise set 2

Exercise set 3

Exercise set 4

Exercise set 5

Exercise set 6

Exercise set 7

Exercise set 8

Exercise set 9


Various files to download

(pdf files)

Syllabus

Schedule of remaining lectures

 

Last update: 24.05.11