P-adic distribution of cm points and hecke orbits i: Convergence towards the gauss point

SEBASTIAN DANIEL HERRERO MIRANDA, Ricardo Menares, Juan Rivera-Letelier

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Abstract

We study the asymptotic distribution of CM points on the moduli space of elliptic curves over Cp, as the discriminant of the underlying endomorphism ring varies. In contrast with the complex case, we show that there is no uniform distribution. In this paper we characterize all the sequences of discriminants for which the corresponding CM points converge towards the Gauss point of the Berkovich affine line. We also give an analogous characterization for Hecke orbits. In the companion paper we characterize all the remaining limit measures of CM points and Hecke orbits.

Original languageEnglish
Pages (from-to)1239-1290
Number of pages52
JournalAlgebra and Number Theory
Volume14
Issue number5
DOIs
StatePublished - 2020
Externally publishedYes

Keywords

  • Elliptic curves
  • Equidistribution
  • Hecke correspondences

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