On a question of Frey and Jarden about the rank of Abelian varieties

DOI10.1016/j.jnt.2005.12.006zbMath1193.11059OpenAlexW2036424679MaRDI QIDQ2472391

Sebastian Petersen

Publication date: 21 February 2008

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2005.12.006

zbMATH Keywords

rankAbelian varietyHilbertian fieldgeneralized specialization theorem

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Arithmetic ground fields for abelian varieties (14K15)

Related Items

The rank of hyperelliptic Jacobians in families of quadratic twists ⋮ Ramified covers of abelian varieties over torsion fields ⋮ Definability and decidability for rings of integers in totally imaginary fields ⋮ Density of rational points on del Pezzo surfaces of degree one ⋮ ON THE RANK OF ABELIAN VARIETIES OVER AMPLE FIELDS

Cites Work

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• On the rational points of some Jacobian varieties over large algebraic number fields
• A remark on the rank of Jacobians of hyperelliptic curves over \({\mathbb{Q}}\) over certain elementary abelian 2-extensions
• The rank of abelian varieties over large algebraic fields
• Rational points of Abelian varieties with values in towers of number fields
• Rank Frequencies for Quadratic Twists of Elliptic Curves
• Ranks of elliptic curves
• Mordell-Weil rank of the jacobians of the curves defined by $y^p = f(x)$
• RANK OF ELLIPTIC CURVES OVER ALMOST SEPARABLY CLOSED FIELDS
• Heights and the specialization map for families of abelian varieties.
• Approximation Theory and the Rank of Abelian Varieties Over Large Algebraic Fields
• Varieties Defined by Quadratic Equations
• Problèmes arithmétique et géométriques rattachés à la notion de rang d'une courbe algébrique dans un corps
• The rank of abelian varieties over infinite Galois extensions