Arithmetic finiteness of very irregular varieties
Algebraic Geometry
2026-03-12 v5 Number Theory
Abstract
We prove the Shafarevich conjecture for very irregular varieties of dimension less than half the dimension of their Albanese variety, subject to some mild numerical conditions. Our proof relies on the Lawrence-Venkatesh method as in the work of Lawrence-Sawin, together with the big monodromy criterion from our work with Javanpeykar and Lehn.
Keywords
Cite
@article{arxiv.2310.08485,
title = {Arithmetic finiteness of very irregular varieties},
author = {Thomas Krämer and Marco Maculan},
journal= {arXiv preprint arXiv:2310.08485},
year = {2026}
}
Comments
Final version, to appear in Duke Math. J