Adrian Langer

I will talk about an analogue of Hodge theory in positive characteristic. In particular, I will show analogues of Schmid's  nilpotent orbit theorem and nearby cycles in positive characteristic. As an application I will prove some strong semipositivity theorems for analogs of complex polarized variations of Hodge structures. This implies, e.g., semipositivity for relative canonical divisor of a semistable reduction and implies some new results over complex numbers.