Higher Algebraic K-Theory


Masters course of the Section of mathematics 
Fall 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. In this course we take a homotopy-theoretic approach to the definition of the algebraic K-theory groups.

Schedule

Lectures: Tuesdays, 8:15 to 10:00

Exercices: Tuesdays, 10:15 to 12:00

Room: MA 10
 

Syllabus

I. Essential category theory
II. Simplicial methods in category theory
III. Quillen's K-theory of exact categories
IV. Waldhausen K-theory

Bibliography


Daniel Quillen, Higher Algebraic K-theory I, Springer LNM 341, 1973.

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

Marco Schlichting, Higher Algebraic K-theory (after Quillen, Thomason and others), Springer LNM 2008, 2011.

Friedhelm Waldhausen, Algebraic K-theory of spaces, Springer LNM 1126, 1985.

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

Exercise set 10

Exercise set 11

Various files to download

(pdf files)

Detailed syllabus

 

Last update: 15.12.2011