English

Uniform Bogomolov Conjecture for Tori

Number Theory 2025-07-15 v7 Algebraic Geometry

Abstract

In this paper, we present a novel proof of the uniform Bogomolov conjecture for algebraic tori. To do this, we introduce a definition of non-degenerate subvarieties applicable to a family of algebraic tori and establish an equidistribution theorem in this setting. Our method stems from recent advancements in the uniform Mordell-Lang conjecture, particularly the breakthrough results by Dimitrov, Gao, and Habegger, as well as independent work by K\"uhne and the collaborative effort of Gao, Ge, and K\"uhne.

Keywords

Cite

@article{arxiv.2311.15763,
  title  = {Uniform Bogomolov Conjecture for Tori},
  author = {Ruida Di},
  journal= {arXiv preprint arXiv:2311.15763},
  year   = {2025}
}