Masters course of the Section of mathematics
Spring 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.
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.
Lectures: Fridays, 8:15 to 10:00
Exercices: Fridays, 10:15 to 12:00
Room: MA 12
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
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).
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
Schedule of remaining lectures
Last update: 24.05.11