English

Prym varieties and cubic threefolds over $\mathbb{Z}$

Algebraic Geometry 2024-09-25 v1

Abstract

We develop a theory of Prym varieties and cubic threefolds over fields of characteristic 22. As an application, we prove that smooth cubic threefolds are non-rational over an arbitrary field and solve a conjecture of Deligne regarding arithmetic Torelli maps. We also prove the Torelli theorem for cubic threefolds over arbitrary fields.

Keywords

Cite

@article{arxiv.2409.15580,
  title  = {Prym varieties and cubic threefolds over $\mathbb{Z}$},
  author = {Tudor Ciurca},
  journal= {arXiv preprint arXiv:2409.15580},
  year   = {2024}
}
R2 v1 2026-06-28T18:54:34.045Z