Coates-Wiles towers in dimension two

DOI10.1007/BF01462890zbMath0726.11039MaRDI QIDQ802659

David Grant

Publication date: 1988

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

Full work available at URL: https://eudml.org/doc/164488

zbMATH Keywords

conductorcomplex multiplicationabelian surfaceCoates-Wiles theoremgeneralized Kummer extensions

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15) Arithmetic ground fields for abelian varieties (14K15) Algebraic number theory: global fields (11R99)

Cites Work

• Congruences for special values of L-functions of elliptic curves with complex multiplication
• Ramification in the Coates-Wiles tower
• Global units and ideal class groups
• Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
• On the conjecture of Birch and Swinnerton-Dyer
• Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer
• Good reduction of abelian varieties
• On the zeta-function of an abelian variety with complex multiplication
• The Determination of all Imaginary, Quartic, Abelian Number Fields With Class Number 1
• Automorphisms of finite groups
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