English

Images of abelian schemes

Algebraic Geometry 2024-12-20 v2

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.

Keywords

Cite

@article{arxiv.2312.13262,
  title  = {Images of abelian schemes},
  author = {Jeff Achter and Sebastian Casalaina-Martin and Jonathan Wise},
  journal= {arXiv preprint arXiv:2312.13262},
  year   = {2024}
}

Comments

Complete 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