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

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 prov...

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Veröffentlicht in:Comptes Rendus. Mathématique 2010, Vol.348 (1), p.9-10
Hauptverfasser: Perucca, Antonella, Jossen, Peter
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1631-073X