Continuity of heights in families and complete intersections in toric varieties
Number Theory
2024-12-23 v1 Algebraic Geometry
Logic
Abstract
We study the variation of heights of cycles in flat families over number fields or, more generally, globally valued fields. To a finite type scheme over a GVF we associate a locally compact Hausdorff space which we refer to as its GVF analytification. For a flat projective family, we prove that the height of fibres is a continuous function on the GVF analytification of the base. As an application, we prove Roberto Gualdi's conjecture on limit heights of complete intersections in toric varieties.
Cite
@article{arxiv.2412.15988,
title = {Continuity of heights in families and complete intersections in toric varieties},
author = {Pablo Destic and Nuno Hultberg and Michał Szachniewicz},
journal= {arXiv preprint arXiv:2412.15988},
year = {2024}
}
Comments
33 pages, comments welcome!