On canonical subgroups of Hilbert–Blumenthal abelian varieties

Shin Hattori

doi:10.5802/jtnb.1029

Shin Hattori ¹

¹Department of Natural Sciences, Tokyo City University 1-28-1 Tamazutsumi Setagaya-ku, Tokyo, Japan

Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 2, pp. 355-391

Abstract (Original language)
Résumé

Let $p$ be a rational prime. Let $F$ be a totally real number field which is unramified over $p$ . In this paper, we develop a theory of canonical subgroups for Hilbert–Blumenthal abelian varieties with $𝒪_{F}$ -actions, in which they are related with Hodge–Tate maps if the $β$ -Hodge height is less than $(p - 1) / p^{n}$ for every embedding $β : F \to {\bar{ℚ}}_{p}$ .

Soit $p$ un nombre premier. Soit $F$ un corps totalement réel non ramifié en $p$ . Dans cet article, nous développons une théorie de sous-groupes canoniques pour les variétés abéliennes de Hilbert–Blumenthal avec $𝒪_{F}$ -actions, dans laquelle ceux-ci sont liés à des applications de Hodge–Tate si la $β$ -hauteur de Hodge est plus petite que $(p - 1) / p^{n}$ pour tout plongement $β : F \to {\bar{ℚ}}_{p}$ .

Article information
Cite this article

Received: 2016-07-13
Revised: 2017-03-02
Accepted: 2017-04-06
Published online: 2018-12-06

MR Zbl

DOI: 10.5802/jtnb.1029

Classification: 11G10, 14L15
Keywords: Hilbert–Blumenthal abelian variety, canonical subgroup

Author's affiliations:

Shin Hattori ¹

¹ Department of Natural Sciences, Tokyo City University 1-28-1 Tamazutsumi Setagaya-ku, Tokyo, Japan

License:

CC-BY-ND 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

Shin Hattori. On canonical subgroups of Hilbert–Blumenthal abelian varieties. Journal de théorie des nombres de Bordeaux, Volume 30 (2018) no. 2, pp. 355-391. doi: 10.5802/jtnb.1029

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