Connectedness results for $l$-adic representations associated to abelian varieties

A. Silverberg; Yu G. Zarhin

Displaying similar documents to “Connectedness results for $l$ -adic representations associated to abelian varieties”

Abelian varieties over fields of finite characteristic

Yuri Zarhin (2014)

Open Mathematics

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The aim of this paper is to extend our previous results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.

Semistable reduction and torsion subgroups of abelian varieties

Alice Silverberg, Yuri G. Zarhin (1995)

Annales de l'institut Fourier

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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...