Moritz Kerz (U Regensburg): Cohomology of local systems

We study local systems on algebraic varieties. The cohomology with coefficients in these local systems reflects important properties of the topology of complex algebraic varieties, for example we know the Hard Lefschetz theorem and interesting properties about jumping loci. In the talk I will give an overview about the classical case of varieties over the field of complex numbers and I will explain what we know about positive characteristic.