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| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Journal de Théorie des Nombres de Bordeaux |
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| Verlag: | UNIV BORDEAUX, INST MATHEMATIQUES BORDEAUX |
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| Ort der Veröffentlichung: | TALENCE |
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| Band: | 27 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 3 |
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| Seitenbereich: | S. 805-814 |
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| Datum: | 2015 |
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| Institutionen: | Mathematik |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.5802/jtnb.924 | DOI |
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| Stichwörter / Keywords: | GSP; |
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| Dewey-Dezimal-Klassifikation: | 600 Technik, Medizin, angewandte Wissenschaften > 610 Medizin |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 60730 |
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Zusammenfassung
Let A, A' be elliptic curves or abelian varieties fully of type GSp defined over a number field K. This includes principally polarized abelian varieties with geometric endomorphism ring Z and dimension 2 or odd. We compare the number of points on the reductions of the two varieties. We prove that A and A' are K-isogenous if the following condition holds for a density-one set of primes p of K: the ...
Zusammenfassung
Let A, A' be elliptic curves or abelian varieties fully of type GSp defined over a number field K. This includes principally polarized abelian varieties with geometric endomorphism ring Z and dimension 2 or odd. We compare the number of points on the reductions of the two varieties. We prove that A and A' are K-isogenous if the following condition holds for a density-one set of primes p of K: the prime numbers dividing #A(k(p)) also divide #A'(k(p)). We generalize this statement to some extent for products of such varieties. This refines results of Hall and Perucca (2011) and of Ratazzi (2012).
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