Motives and (super-)representation theory: principles and case studies
By Yves André
Finiteness Questions for Étale Coverings with Bounded Wild Ramification at the Boundary
By Vasudevan Srinivas
Appears in collections : Higher dimensional algebraic geometry and characteristic p > 0 / Géométrie algébrique en dimension supérieure et caractéristique p > 0, Exposés de recherche
I will first introduce K3 surfaces and determine their algebraic deRham cohomology. Next, we will see that crystalline cohomology (no prior knowledge assumed) is the "right" replacement for singular cohomology in positive characteristic. Then, we will look at one particular class of K3 surfaces more closely, namely, supersingular K3 surfaces. These have Picard rank 22 (note: in characteristic zero, at most rank 20 is possible) and form 9-dimensional moduli spaces. For supersingular K3 surfaces, we will see that there exists a period map and a Torelli theorem in terms of crystalline cohomology. As an application of the crystalline Torelli theorem, we will show that a K3 surface is supersingular if and only if it is unirational.