Department Mathematik



Yorck Sommerhäuser



  • Winter semester 2002/2003
  • Time: Friday, 2:15 pm
  • Room: E 45
  • Planning session: Friday, October 18, 2002, 2:15 pm, Room E 45
  • Contents: In this seminar we give an introduction to K-theory. K-theory is a part of ring theory that assigns to every ring certain abelian groups, the so-called K-groups, that describe certain properties of the ring. The origin of this theory lies in topology, where the base ring is the ring of continuous functions on a topological space. The K-groups then become invariants of the topological space.

    The focus of the seminar will be on algebraic K-theory, which, however, will be compared with topological K-theory and the K-theory of operator algebras. A central topic of the seminar is the connection between the second K-group and the Brauer group, which is given by the Merkuriev-Suslin theorem. From this theorem, we will proceed on the one hand to the discussion of the new progress in motivic cohomology that has recently attracted attention, on the other hand to the consideration of the role that K-theory plays in string theory.

    The seminar is addressed at graduate students who want to learn about a subject that is relevant for algebra, topology, and differential geometry. Besides a certain mathematical maturity, there are no special prerequisites necessary.

  • Seminar program (german, dvi)
  • Internet references:
    1. V. Voevodsky: Lectures on motivic cohomology (Notes by P. Deligne)
    2. V. Voevodsky: On 2-torsion in motivic cohomology
    3. Internet page of the seminar at the `Institute of Advanced Study'