A counterexample to the local-global principle of linear dependence for Abelian varieties

Let A be an Abelian variety defined over a number field k. Let P be a point in A(k) and let X be a subgroup of A(k). Gajda and Kowalski asked in 2002 whether it is true that the point P belongs to X if and only if the point (P mod p) belongs to (X mod p) for all but finitely many primes p of k. We provide a counterexample. (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.


Published in:
Comptes Rendus Mathematique, 348, 9-10
Year:
2010
Keywords:
Laboratories:




 Record created 2011-12-16, last modified 2018-03-17


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