Hall, Chris and Perucca, Antonella (2013) CHARACTERIZING ABELIAN VARIETIES BY THE REDUCTION OF THE MORDELL-WEIL GROUP. PACIFIC JOURNAL OF MATHEMATICS, 265 (2). pp. 427-440. ISSN 0030-8730,
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Let A be an abelian variety defined over a number field K. Let p be a prime of K of good reduction and A(p) the fiber of A over the residue field k(p). We call A(K)(p) the image of the Mordell-Weil group via reduction modulo p, which is a subgroup of A(p)(k)(p). We prove in particular that the size of A(K)(p), by varying p, encodes enough information to characterize the K-isogeny class of A, provided that the following necessary condition holds: the Mordell-Weil group A(K) is Zariski dense in A. This is an analogue a 1983 result of Faltings, considering instead the size of A(p)(k(p)).
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ORDER; POINT; abelian varieties; Mordell-Weil group |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 31 Mar 2020 10:15 |
| Last Modified: | 31 Mar 2020 10:15 |
| URI: | https://pred.uni-regensburg.de/id/eprint/15991 |
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