**Cours spécialisé ** (GA, GT, TA)

# Algebraic K-theory and motivic cohomology

### Maria Yakerson

** Contact :** `maria.yakerson à imj-prg.fr`

Pas de notes de cours prévues.

## Présentation

Algebraic K-theory is a rich invariant of rings and, more generally, schemes, which has homotopic nature. It encodes intrinsic information about vector bundles on a scheme. Algebraic K-theory appears in (conjectural) answers to a priori unrelated questions in number theory and differential topology, and there are lots of conjectures about properties of K-theory and its computations. In this course, we will analyze algebraic K-theory of (smooth) schemes via a filtration by motivic cohomology groups, which can be thought of as a generalization of Chow groups, and discuss its connection with etale cohomology groups.

## Contenu

- algebraic K-theory
- Chow groups
- motivic cohomology

## Prérequis

The prerequisites are: scheme theory, homotopy theory, basic category theory. I recommend taking the courses Schemas I and Homotopie II.
## Bibliographie

- Eric M. Friedlander, Daniel R. Grayson. Handbook of K-Theory.
* Springer-Verlag Berlin, Heidelberg 2005.*