Algebraic K-Theory

Masters course – Spring 2013

 

Prof. Kathryn Hess Bellwald

Assistant: Dimitri Zaganidis

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 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.

Schedule

  • Lectures: Thursday, 13:15 to 15:00
  • Exercices: Thursday, 15:15 to 17:00
  • Room: MA 11

Syllabus

 
  1. K0 : Grothendieck groups, stability, tensor products, change of rings
  2. K1 : elementary matrices, commutators and determinants

 

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.

Joseph Rotman, An Introduction to Homological Algebra, Academic Press, 1979.

Charles Weibel, The K-book: An Introduction to Algebraic K-theory, (in progress).

Homework sets

   The course wiki, where all exercise sets and the course syllabus can be found.