Semistable reduction and torsion subgroups of abelian varieties

Alice Silverberg; Yuri G. Zarhin

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Abelian varieties over fields of finite characteristic

Yuri Zarhin (2014)

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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.

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)

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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.

A construction of an abelian variety with a given endomorphism algebra

F. Oort, M. Van der Put (1988)

Compositio Mathematica

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On the prime-to- $p$ part of the groups of connected components of Néron models

Bas Edixhoven (1995)

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Abelian varieties over finite fields with a specified characteristic polynomial modulo $ℓ$

Joshua Holden (2004)

Journal de Théorie des Nombres de Bordeaux

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We estimate the fraction of isogeny classes of abelian varieties over a finite field which have a given characteristic polynomial $P (T)$ modulo $ℓ$ . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order $ℓ$ .

Displaying similar documents to “Semistable reduction and torsion subgroups of abelian varieties”

Abelian varieties over fields of finite characteristic

Torsion points on abelian varieties of CM-type

Abelian varieties-Galois representation and properties of ordinary reduction

A Note on height pairings on polarized abelian varieties

A construction of an abelian variety with a given endomorphism algebra

On the prime-to- p part of the groups of connected components of Néron models

Abelian varieties over finite fields with a specified characteristic polynomial modulo ℓ

On the prime-to- $p$ part of the groups of connected components of Néron models

Abelian varieties over finite fields with a specified characteristic polynomial modulo $ℓ$