Abelian varieties-Galois representation and properties of ordinary reduction
Rutger Noot (1995)
Compositio Mathematica
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Displaying similar documents to “Corestriction of central simple algebras and families of Mumford-type”
Abelian varieties-Galois representation and properties of ordinary reduction
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 be an abelian variety defined over a number field . 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.
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 has a maximal isotropic subgroup of -torsion points all of which are defined over , and , then the abelian variety has semistable reduction away from . This result can be viewed as an extension of Raynaud’s theorem that if an abelian variety and all its -torsion points are defined over a field and , then the abelian variety has semistable reduction away from . We also give information about the Néron...
On the image of -adic Galois representations for abelian varieties of type I and II.
Banaszak, G., Gajda, W., Krasoń, P. (2007)
Documenta Mathematica
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A construction of an abelian variety with a given endomorphism algebra
F. Oort, M. Van der Put (1988)
Compositio Mathematica
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Abelian varieties over finite fields with a specified characteristic polynomial modulo
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 modulo . As an application we find the proportion of isogeny classes of abelian varieties with a rational point of order .