Abelian varieties-Galois representation and properties of ordinary reduction
Rutger Noot (1995)
Compositio Mathematica
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Rutger Noot (1995)
Compositio Mathematica
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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.
Alice Silverberg (1988)
Compositio Mathematica
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Qian Lin, Ming-Xi Wang (2015)
Acta Arithmetica
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We prove that if a curve of a nonisotrivial family of abelian varieties over a curve contains infinitely many isogeny orbits of a finitely generated subgroup of a simple abelian variety, then it is either torsion or contained in a fiber. This result fits into the context of the Zilber-Pink conjecture. Moreover, by using the polyhedral reduction theory we give a new proof of a result of Bertrand.
Jeffrey D. Achter (2012)
Journal de Théorie des Nombres de Bordeaux
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Let be an absolutely simple abelian variety over a number field; we study whether the reductions tend to be simple, too. We show that if is a definite quaternion algebra, then the reduction is geometrically isogenous to the self-product of an absolutely simple abelian variety for in a set of positive density, while if is of Mumford type, then is simple for almost all . For a large class of abelian varieties with commutative absolute endomorphism ring, we give an explicit...
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.
Banaszak, G., Gajda, W., Krasoń, P. (2007)
Documenta Mathematica
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