GAAG seminar - Differential forms for singular varieties

The sheaf of differential forms is a very useful tool in many parts of algebraic geometry. For example it can be used to define invariants like the genus
or the Kodaira dimension. By definition, it is not well behaved for singular varieties, leading to several ad hoc work arounds. We propose a systematic approach: sheafification in the cdh-topology. This is a Grothendieck topology introduced by Voevodsky. It is particularly well-suited to questions on algebraic cycles. We will discuss the situation with differential forms, both in characteristic 0 and in positive characteristic.