# Short course "Motivic Cohomology". Lecture 2: Motivic cohomology and triangulated categories of motives

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Speaker:

Marc Levine
Affiliation:

University Duisburg-Essen
Date:

Tue, 07/03/2023 - 09:30 - 11:00
Location:

MPIM Lecture Hall Lecture 2/3.

We introduce motivic cohomology as maps in Voevodsky’s triangulated category of motives. We describe the comparison theorem identifying motivic cohomology with Bloch’s higher Chow groups and discuss the relation of mod n-motivic cohomology with étale cohomology. We use the comparison theorem to show how the category of Chow motives fully embeds in the category of geometric motives and briefly describe realization functors associated to de Rham cohomology and Betti (co)homology.

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