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

Let ASA \rightarrow S be an abelian scheme over a pp-adic field, and let s ⁣:SAs \colon S \rightarrow A be a section. We study the torsion locus n1s1(A[n])\bigcup \limits_{n \geq 1} s^{-1}(A[n]) on SS, and we show that torsion points on SS of different orders stay away from each other.

Cite this article

Brian Lawrence, Umberto Zannier, On the pp-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