## Lecture Series "Triangulated categories of motivic sheaves", 25-28 February 2020, Universität Freiburg

Cohomology theories in algebraic geometry do not come alone, but with associated "sheaf theories" and a rich functoriality with respect to morphisms of schemes ("six operation formalism"). The archetypal example is the theory of étale and l-adic sheaves developed in SGA4-5, which has been adapted to many other settings (analytic sheaves, D-modules, etc.) Thanks to the work of Voevodsky and his successors, we now have a theory of triangulated categories of étale motivic sheaves which generalises the theory of étale sheaves and is, in some sense, the universal such (triangulated) sheaf theory. Surprisingly, morphism groups in these categories are related to algebraic cycles. In this course, I will first explain the construction of these categories and develop their functoriality. I will then describe some of the related conjectures which promise tannakian insights into the structure of algebraic cycles, and I will end with the particular case of 1-motivic sheaves, coming from relative curves, where everything is well-understood.

- Lecture Series
- Feb 25, 2020 10:15 AM to Feb 28, 2020 11:45 AM.