Year: 2025
Type: preprint
Abstract: Let $A/\mathbb{Q}$ be an abelian variety and let $\hat{h}$ be the canonical height on $A(\overline{\Q})$ associated to a symmetric ample line bundle $\mathcal{L}$ on $A$. We prove that $\hat h$ is bounded away from zero on non-torsion points of $A$ defined over the maximal totally $p$-adic extension of $\mathbb{Q}$, for all but finitely many primes $p$. More generally, for abelian varieties over a number field $K$, we obtain a similar height gap over certain infinite extensions of $K$, including Galois extensions with finite local degree at non-archimedean places.
Source: arXiv (Cornell University)
Author: Kala, Sushant
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106740276
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