Program of the baby seminar WS 2015/2016 on The K-Theory of Fields

AbstractNo Abstract Found

The aim of the seminar is understand the Higher K-Theory of fields. We will start from recalling the classical K-Theory and the construction for the higher K-theory as the homotopy groups of \(BGL(R)^{+}\) given by Quillen.

Main Theorems

Plan of the Talks

Introduction to K-theory

Talk 1: Higher Algebriac K-theory

In this talk the speaker should recall the definition of Higher K-Theory for rings. Explain the \(BGL^{+}\) definition for rings. The speaker should recall the basic properties of the K-theory with out proofs.

  • Porduct structure in the K-theory and the structure of \(H\)-space

  • Localization theorem

  • Projective Bundle Formula

  • Fundamental exact sequence

  • Genstern resolution for smooth-semilocal ring over \(k\).

  • The speaker should explain why it is important compute the K-theory of algebraically closed fields.

  • Also it would be nice to give explicity computations of