English

Putting the p back in Prym

Algebraic Geometry 2024-12-20 v2 Number Theory

Abstract

After Jacobians of curves, Prym varieties are perhaps the next most studied abelian varieties. They turn out to be quite useful in a number of contexts. For technical reasons, there does not appear to be any systematic treatment of Prym varieties in characteristic 2, and due to our recent interest in this topic, the purpose of this paper is to fill in that gap. Our main result is a classification of branched covers of curves in characteristic 2 that give rise to Prym varieties. We are also interested in the case of Prym varieties in the relative setting, and so we develop that theory here as well, including an extension of Welters' Criterion.

Keywords

Cite

@article{arxiv.2312.13263,
  title  = {Putting the p back in Prym},
  author = {Jeff Achter and Sebastian Casalaina-Martin},
  journal= {arXiv preprint arXiv:2312.13263},
  year   = {2024}
}

Comments

Major rewrite triggered by issues with V1 of arXiv:2312.13262. Statements for covers of curves are unchanged; some general statements (on norms and complements) now proved under additional hypothesis

R2 v1 2026-06-28T13:57:53.516Z