Algebraic K-Theory

Masters course – Spring 2011

Prof. Kathryn Hess Bellwald
Assistant: Eric Finster


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. 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.

Schedule

  • Lectures: Fridays, 8:15 to 10:00
  • Exercices: Fridays, 10:15 to 12:00
  • Room: MA 12

Syllabus

  1. Elementary category theory and module theory
  2. K0 : Grothendieck groups, stability, tensor products, change of rings
  3. K1 : elementary matrices, commutators and determinants
  4. K2: Steinberg symbols, exact sequences, Matsumoto’s theorem

 

Bibliography

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).

Various files to download

 

Last update: 24.05.11