On the rational points of abelian varieties over \({\mathbb{Z}}_ p\)- extensions of number fields

DOI10.1007/BF01456190zbMath0657.14024MaRDI QIDQ1110605

Kay Wingberg

Publication date: 1987

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164306

zbMATH Keywords

abelian varietyMordell-Weil groupcomplex multiplicationIwasawa algebra\({\mathbb{Z}}_ p\)-extensionrational points of a toroidal formal groupuniversal norms of a commutative formal group

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for abelian varieties (14K15) Complex multiplication and abelian varieties (14K22) Cyclotomic extensions (11R18) Formal groups, (p)-divisible groups (14L05)

Related Items (9)

Finite \(\Lambda\)-submodules of Selmer groups of Abelian varieties over cyclotomic \(\mathbb Z_p\)-extensions. ⋮ On the weak Leopoldt conjecture and coranks of Selmer groups of supersingular abelian varieties in \(p\)-adic Lie extensions ⋮ Torsion of abelian varieties over GL(2)-extensions of number fields ⋮ A remark on the 𝔐_H(G)-conjecture and Akashi series ⋮ A generalization of a theorem of Imai and its applications to Iwasawa theory ⋮ Sur une forme faible de la conjecture de Greenberg II ⋮ Some remarks on pseudo-null submodules of tamely ramified Iwasawa modules ⋮ Bounding the Iwasawa invariants of Selmer groups ⋮ A weak form of Greenberg's generalized conjecture for imaginary quadratic fields

Cites Work

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• The norm map for ordinary Abelian varieties
• Finiteness theorems for abelian varieties over number fields.
• Arithmetic of formal groups and applications. I: Universal norm subgroups
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• Rational points of Abelian varieties with values in towers of number fields
• Arithmétique des courbes elliptiques et théorie d'Iwasawa
• Division fields of abelian varieties with complex multiplication
• A remark on the rational points of abelian varieties with values in cyclotomic $Z_p$-extensions

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