K(K)
Henri Gillet, University of Illinois at Chicago, henri@math.uic.edu
Building on the work of many others, including: LeComte, Schechtmann, Suslin,
Paluch, Soulé and the author, and in particular the computations done
in the "classical" case of topological K-theory, I shall describe a method of
computing the algebraic K-theory of algebraic K-theory, i.e., the ring of
operations on K-theory. That is, working in the homotopy category of
simplicial sheaves we shall compute the K-theory of one of the simplicial
sheaves, such as the "G-construction" of D. Grayson and the author,
representing K-theory. One difference between this and the previous work is
that I shall work integrally, and shall try to avoid problems with
stabilization. The point is not so much new results as to have a conceptual
approach.