Cours spécialisé (GA, GT, TA)

Algebraic K-theory and motivic cohomology

Maria Yakerson

Contact : maria.yakerson à

Pas de notes de cours prévues.


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.



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