Images of abelian schemes

Abstract

We provide some conditions for the image of a morphism of abelian schemes to again be an abelian scheme. For context, in characteristic 0, the image is always an abelian scheme; in mixed and positive characteristic the image can fail to be an abelian scheme, and so it is in this setting that the conditions we provide are pertinent.

arXiv commentComplete rewrite with additional coauthor. Patrick Brosnan alerted us to a serious flaw in the first version. New version gives conditions on the base when the image of an abelian scheme is, or is not, necessarily an abelian scheme