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

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

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

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Resumen

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.

Idioma originalInglés
Páginas (desde-hasta)1239-1290
Número de páginas52
PublicaciónAlgebra and Number Theory
Volumen14
N.º5
DOI
EstadoPublicada - 2020
Publicado de forma externa

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