Generic vanishing in characteristic $p>0$ and the characterization of ordinary abelian varieties (1310.2996v2)

Abstract: We prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of Kawamata's theorems: a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the Albanese map when the Frobenius stable Kodaira dimension is zero.