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
Elementary category theory and module theory
K0 : Grothendieck groups, stability, tensor products, change of rings
K1 : elementary matrices, commutators and determinants