The Picard Group of Corings

Abstract

We introduce the Picard group of corings. We extend the well-known exact sequence from algebras and coalgebras over fields to corings. We extend the Aut-Pic property to corings and we give some new examples of corings having this property. Finally, we give the corresponding exact sequences for the category of entwined modules over an entwining structure, the category of Doi-Koppinen-Hopf modules over a Doi-Koppinen structure, and the category of graded modules by a $G$-set, where $G$ is a group.