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Semistable reduction and torsion subgroups of abelian varieties

Alice Silverberg, Yuri G. Zarhin (1995)

Annales de l'institut Fourier

The main result of this paper implies that if an abelian variety over a field $F$ has a maximal isotropic subgroup of $n$ -torsion points all of which are defined over $F$ , and $n \geq 5$ , then the abelian variety has semistable reduction away from $n$ . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its $n$ -torsion points are defined over a field $F$ and $n \geq 3$ , then the abelian variety has semistable reduction away from $n$ . We also give information about the Néron models...

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Semistable reduction and torsion subgroups of abelian varieties

Shimura Varieties and Twisted Orbital Integrals.

Siegel Cusp Forms as Holomorphic Differential Forms on Certain Compact Varieties.

Small values of the quadratic part of the Néron-Tate height on an abelian variety

Sous-groupes à plusieurs paramètres $p$ -adiques de variétés abéliennes

Sous-groupes canoniques et cycles évanescents p-adiques pour les variétés abéliennes

Stable reduction and uniformization of abelian varieties II.

Sur des hauteurs alternatives. I.

Sur les mauvais facteurs locaux des fonctions L attachées aux surfaces abéliennes et surfaces K-3

Systematic Growth of Mordell-Weil Groups of Abelian Varieties in Towers of Number Fields.

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