Tate–Shafarevich groups in anticyclotomic ℤp-extensions at supersingular primes

DOI10.1112/S0010437X08003874zbMath1257.11055OpenAlexW2051304717MaRDI QIDQ3628242

Mirela Ciperiani

Publication date: 19 May 2009

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1112/s0010437x08003874

zbMATH Keywords

elliptic curvesHeegner pointsSelmer groupsupersingular reduction

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Iwasawa theory (11R23)

Related Items (9)

On the weak Leopoldt conjecture and coranks of Selmer groups of supersingular abelian varieties in \(p\)-adic Lie extensions ⋮ Asymptotic formula for Tate-Shafarevich groups of \(p\)-supersingular elliptic curves over anticyclotomic extensions ⋮ Supersingular elliptic curves over \(\mathbb{Z}_p\)-extensions ⋮ Selmer Groups and AnticyclotomicZ_p-extensions ⋮ Fine Selmer groups, Heegner points and anticyclotomic ℤp-extensions ⋮ Plus/minus Selmer groups and anticyclotomic \(\mathbb{Z}_p\)-extensions ⋮ Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes ⋮ \(\Lambda\)-submodules of finite index of anticyclotomic plus and minus Selmer groups of elliptic curves ⋮ Kolyvagin's work and anticyclotomic tower fields: the supersingular case

Cites Work

• Solvable points on genus one curves
• On \(L\)-functions of elliptic curves and cyclotomic towers
• \(p\)-adic height pairings. II
• On the main conjecture of Iwasawa theory for imaginary quadratic fields
• Iwasawa theory for elliptic curves at supersingular primes
• On the Tate-Shafarevich groups over cyclotomic fields of an elliptic curve with supersingular reduction. I.
• Mazur's conjecture on higher Heegner points.
• An algebraic version of a theorem of Kurihara
• Special values of anticyclotomic \(L\)-functions.
• Modular elliptic curves and Fermat's Last Theorem
• Galois properties of points of finite order of elliptic curves
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Fonctions $L$ $p$-adiques, théorie d'Iwasawa et points de Heegner

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