Masters course – Spring 2013
Prof. Kathryn Hess Bellwald
Assistant: Dimitri Zaganidis
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 two of these groups.
Applications of algebraic K-theory to number theory, algebraic topology, algebraic geometry, representation theory and functional analysis will be briefly sketched as well.
- Lectures: Thursday, 13:15 to 15:00
- Exercices: Thursday, 15:15 to 17:00
- Room: MA 11
- K0 : Grothendieck groups, stability, tensor products, change of rings
- K1 : elementary matrices, commutators and determinants
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.
Joseph Rotman, An Introduction to Homological Algebra, Academic Press, 1979.
Charles Weibel, The K-book: An Introduction to Algebraic K-theory, (in progress).
The course wiki, where all exercise sets and the course syllabus can be found.