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

Brian Lawrence; Umberto Zannier

doi:10.4171/rlm/891

JournalsrlmVol. 31, No. 2pp. 285–295

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

Brian Lawrence
University of Chicago, USA
Umberto Zannier
Scuola Normale Superiore, Pisa, Italy

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Abstract

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

Cite this article

Brian Lawrence, Umberto Zannier, On the $p$ -adic distribution of torsion values for a section of an abelian scheme. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 2, pp. 285–295

DOI 10.4171/RLM/891