On canonical subgroups of Hilbert–Blumenthal abelian varieties
Journal de Théorie des Nombres de Bordeaux, Volume 30 (2018) no. 2, pp. 355-391.

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 ¯ 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 ¯ p .

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Accepted:
Published online:
DOI: 10.5802/jtnb.1029
Classification: 11G10,  14L15
Keywords: Hilbert–Blumenthal abelian variety, canonical subgroup
Shin Hattori 1

1 Department of Natural Sciences, Tokyo City University 1-28-1 Tamazutsumi Setagaya-ku, Tokyo, Japan
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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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1029/

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