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Linear dependence in Mordell-Weil groups
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Wojciech Gajda
Published/Copyright:
March 31, 2009
Abstract
Let A be an abelian variety defined over a number field F. Let P be a point in the Mordell-Weil group A(F) and H a subgroup of A(F). We consider the following local-global principle originated with the support problem of Erdös for the integers: the point P belongs to the group H, if for almost all primes v of F, the point P (modulo v) belongs to the group H (modulo v). We prove that the principle holds for any abelian variety A, if H is a free submodule and the point P generates a free submodule of A(F) over the ring EndFA.
Received: 2006-06-12
Revised: 2008-10-29
Published Online: 2009-03-31
Published in Print: 2009-May
© Walter de Gruyter Berlin · New York 2009
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Articles in the same Issue
- Gröbner geometry of vertex decompositions and of flagged tableaux
- The Diophantine equation aX4 – bY2 = 1
- C*-algebras and self-similar groups
- Conjugate varieties with distinct real cohomology algebras
- Classification of hyperfinite factors up to completely bounded isomorphism of their preduals
- Ricci flow of almost non-negatively curved three manifolds
- Linear dependence in Mordell-Weil groups
Articles in the same Issue
- Gröbner geometry of vertex decompositions and of flagged tableaux
- The Diophantine equation aX4 – bY2 = 1
- C*-algebras and self-similar groups
- Conjugate varieties with distinct real cohomology algebras
- Classification of hyperfinite factors up to completely bounded isomorphism of their preduals
- Ricci flow of almost non-negatively curved three manifolds
- Linear dependence in Mordell-Weil groups
