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arXiv · 2311.15763

Uniform Bogomolov Conjecture for Tori

Ruida Di
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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.

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Ruida Di. 2023-11-27. Uniform Bogomolov Conjecture for Tori. https://arxiv.org/abs/2311.15763

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