On canonical subgroups of Hilbert–Blumenthal abelian varieties

Hattori, Shin

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

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 $\beta$-hauteur de Hodge est plus petite que $(p-1)/p^n$ pour tout plongement $\beta :F\to {\overline{\mathbb{Q}}}_p$.

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 $\beta$-Hodge height is less than $(p-1)/p^n$ for every embedding $\beta :F\to {\overline{\mathbb{Q}}}_p$.

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

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