Higher Algebraic K-Theory
Masters course of the Section of mathematics
Fall semester 2011
Prof. Kathryn Hess Bellwald
Assistant: Eric Finster
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.
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).
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
Last update: 15.12.2011