# 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.

## 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