In this lecture series I will explain how one can use deformation theory to study derived categories in positive characteristic.
I will start by giving an overview on what does it mean to ‘lift’ something ‘to characteristic 0’ and when is this possible. Then I will present a baby example: the study of the Fourier-Mukai partners of products of elliptic curves over algebraically closed fields of characteristic at least 5. After that, I will present Lieblich-Olsson deformation technique which allows us to deform derived equivalence. This is a very versatile tools with many applications (not just in positive characteristic!). I will conclude the series by going over some of these applications in greater details.
These videos were produced by the Hausdorff Center for Mathematics as part of the workshop K3 surfaces, hyperkähler manifolds, and cubic fourfolds.
