Power residues on Abelian varieties |
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Authors: | Siman Wong |
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Institution: | Department of Mathematics and Statistics, University of Massachusetts. Amherst, MA 01003, USA. e-mail: siman@math.umass.edu, US
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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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