We introduce and study a class of objects that encompasses Christensen Foxby’s semidualizing modules complexes Kubik’s quasi-dualizing modules: the [Formula: see text]-adic complexes. give examples equivalent characterizations these objects, including characterization in terms more familiar property. As an application, we proof existence dualizing over complete local rings does not use Cohen St...

A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal stable curve over Mg, specifically, the semi-ampleness of the relative dualizing sheaf, in positive characteristic. An example is given which shows this and the semi-ampleness criterion fail in chara...