Abstract:
Given a prime l and an elliptic curve E defined over a number field k, we show that a non-zero point P∈E(k) lies in lE(k) if and only if P lies in lE(k)(mod ?) for almost all finite primes ? of k. We give conditions on l under which analogous results hold for Abelian varieties and with one point replaced by a finite number of points. We also construct examples to show that these conditions are essential.
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Received: 25 November 1999 / Revised version: 13 January 2000
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Wong, S. Power residues on Abelian varieties. manuscripta math. 102, 129–137 (2000). https://doi.org/10.1007/s002290050008
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DOI: https://doi.org/10.1007/s002290050008