Systematic growth of Mordell-Weil groups of abelian varieties in towers of number fields

DOI10.1007/BF01390224zbMath0429.14013MaRDI QIDQ1137618

Michael Harris

Publication date: 1979

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142625

zbMATH Keywords

abelian varietypoints of infinite orderrank of Mordell-Weil groupstowers of number fields

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves (14H52) Arithmetic ground fields for abelian varieties (14K15)

Related Items (15)

Unnamed Item ⋮ On the structure of Selmer groups over 𝑝-adic Lie extensions ⋮ Arithmétique des courbes elliptiques et théorie d'Iwasawa ⋮ Unnamed Item ⋮ The annihilators of p-adic induced modules ⋮ Rational points on algebraic curves in infinite towers of number fields ⋮ Growth of Selmer rank in nonabelian extensions of number fields ⋮ Unnamed Item ⋮ Iwasawa Theory, projective modules, and modular representations ⋮ Kolyvagin derivatives of modular points on elliptic curves ⋮ The rank of abelian varieties over infinite Galois extensions ⋮ Hecke points on modular curves ⋮ SELF-POINTS ON ELLIPTIC CURVES OF PRIME CONDUCTOR ⋮ Unnamed Item ⋮ On the rank of elliptic curves in elementary cubic extensions

Cites Work

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• \(PGL_ 2\) over the p-adics: its representations, spherical functions, and Fourier analysis
• Galois properties of points of finite order of elliptic curves
• Rational points of Abelian varieties with values in towers of number fields
• Galois Action on Division Points of Abelian Varieties with Real Multiplications
• ELLIPTIC CURVES OF INFINITE RANK OVER Γ-EXTENSIONS

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