Perucca, Antonella (2015) The prime divisors of the number of points on abelian varieties. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 27 (3). pp. 805-814. ISSN 1246-7405,
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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).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | GSP; |
| Subjects: | 600 Technology > 610 Medical sciences Medicine |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 25 Jul 2019 13:09 |
| Last Modified: | 25 Jul 2019 13:09 |
| URI: | https://pred.uni-regensburg.de/id/eprint/6131 |
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