Abstract:  Generic vanishing techniques have proven to be very useful in understanding the geometry of complex irregular varieties (i.e. those with a non-zero holomorphic global 1-form). One example of this is the proof of Ueno’s conjecture K: let X be a smooth complex variety with Kodaira dimension zero, then its Albanese morphism is an algebraic fiber space, and the Kodaira dimension of the general fiber is zero (in particular, Iitaka’s subadditivity conjecture holds for this fibration).

The goal of this talk is to explain this theory in positive characteristic, and give some hints on how these techniques can be used to prove Ueno’s conjecture in this setup.