Abelian varieties over fields of finite characteristic

Yuri Zarhin

Displaying similar documents to “Abelian varieties over fields of finite characteristic”

Torsion points on abelian varieties of CM-type

Alice Silverberg (1988)

Compositio Mathematica

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Abelian varieties-Galois representation and properties of ordinary reduction

Rutger Noot (1995)

Compositio Mathematica

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Galois orbits and equidistribution: Manin-Mumford and André-Oort.

Andrei Yafaev (2009)

Journal de Théorie des Nombres de Bordeaux

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We overview a unified approach to the André-Oort and Manin-Mumford conjectures based on a combination of Galois-theoretic and ergodic techniques. This paper is based on recent work of Klingler, Ullmo and Yafaev on the André-Oort conjecture, and of Ratazzi and Ullmo on the Manin-Mumford conjecture.

Dividing rational points on abelian varieties of CM-type

Kenneth A. Ribet (1976)

Compositio Mathematica

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Factorization estimates for abelian varieties

D. W. Masser, G. Wüstholz (1995)

Publications Mathématiques de l'IHÉS

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A Note on height pairings on polarized abelian varieties

Valerio Talamanca (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $A$ be an abelian variety defined over a number field $k$ . In this short Note we give a characterization of the endomorphisms that preserve the height pairing associated to a polarization. We also give a functorial interpretation of this result.

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...