Department Mathematik



Presheaves with transfers and their cohomology

Winter semester 2021/2

We will study the cohomology groups of smooth schemes with values in a so-called presheaf with (framed) transfers. This is a foundational aspect of a modern branch of algebraic geometry called motivic homotopy theory. We will take a leisurly approach, first reviewing the necessary notions from algebraic geometry (in particular ├ętale, smooth and syntomic morphisms) and homological algebra. Then we will define presheaves with framed transfers, construct examples, and prove the fundamental theorems.

Interested students should register by sending me an email.

Time and place

Fridays 10-12, B252.


A set of notes for the second part of the course can be found here. I will update it regularly.


Voevodsky, Cohomological theory of presheaves with transfers.
Mazza, Voevodsky, Weibel, Lecture notes on motivic cohomology.