Torsion points on abelian varieties of CM-type
Alice Silverberg (1988)
Compositio Mathematica
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Alice Silverberg (1988)
Compositio Mathematica
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Rutger Noot (1995)
Compositio Mathematica
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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.
Kenneth A. Ribet (1976)
Compositio Mathematica
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D. W. Masser, G. Wüstholz (1995)
Publications Mathématiques de l'IHÉS
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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.
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...