Anticyclotomic Iwasawa theory of CM elliptic curves

DOI10.5802/aif.2206zbMath1168.11023arXivmath/0302319OpenAlexW2728775156MaRDI QIDQ877535

Adebisi Agboola, Benjamin Howard

Publication date: 24 April 2007

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0302319

zbMATH Keywords

Iwasawa theorymain conjectureanticyclotomic, \(p\)-adic \(L\)-functionellipic curves

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) Iwasawa theory (11R23)

Related Items (13)

The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions ⋮ The Birch and Swinnerton-Dyer Conjecture: A brief survey ⋮ The vanishing of anticyclotomic \(\mu\)-invariants for non-ordinary modular forms ⋮ The congruent number problem and elliptic curves ⋮ Anticyclotomic Iwasawa theory of abelian varieties of \(\mathrm{GL}_2\)-type at non-ordinary primes ⋮ The -adic Gross–Zagier formula on Shimura curves ⋮ On the control theorem for fine Selmer groups and the growth of fine Tate-Shafarevich groups in \(\mathbb{Z}_p\)-extensions ⋮ On the non-vanishing of \(p\)-adic heights on CM abelian varieties, and the arithmetic of Katz \(p\)-adic \(L\)-functions ⋮ Anticyclotomic \(p\)-ordinary Iwasawa theory of elliptic modular forms ⋮ \(p\)-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin ⋮ On the Eisenstein ideal for imaginary quadratic fields ⋮ \(p^{\infty}\)-Selmer groups and rational points on CM elliptic curves ⋮ Iwasawa μ-Invariants of p-Adic Hecke L-Functions

Cites Work

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• Iwasawa theory and \(p\)-adic heights
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• Dirichlet series and automorphic forms
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• Arithmétique des courbes elliptiques et théorie d'Iwasawa
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• Kolyvagin systems
• Euler Systems
• Anticyclotomic main conjectures for CM modular forms
• The Iwasawa theoretic Gross–Zagier theorem
• On the Birch and Swinnerton-Dyer conjecture
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