*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

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

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

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

**Room: **MA 10

I. Essential category theory

II. Simplicial methods in category theory

III. Quillen's K-theory of exact categories

IV. Waldhausen K-theory

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).

(pdf files)

(pdf files)

Last update: 15.12.2011