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arXiv · 1908.09050

On the $p$-adic distribution of torsion values for a section of an abelian scheme

Brian Lawrence·Umberto Zannier
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Abstract

Let $A \rightarrow S$ be an abelian scheme over a $p$-adic field, and let $s \colon S \rightarrow A$ be a section. We study the torsion locus $\bigcup \limits_{n \geq 1} s^{-1}(A[n])$ on $S$, and we show that torsion points on $S$ of different orders stay away from each other.

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Brian Lawrence, Umberto Zannier. 2019-08-23. On the $p$-adic distribution of torsion values for a section of an abelian scheme. https://arxiv.org/abs/1908.09050

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