Solvable points on genus one curves

DOI10.1215/00127094-2008-010zbMath1168.14014OpenAlexW2025270760WikidataQ116141757 ScholiaQ116141757MaRDI QIDQ925699

Andrew Wiles, Mirela Ciperiani

Publication date: 22 May 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/efef767f4f8bee2aa60284f3a4ba96734560ee7d

zbMATH Keywords

rational pointscurvessolvable extensions

Mathematics Subject Classification ID

Rational points (14G05) Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Iwasawa theory (11R23) Galois cohomology (11R34)

Related Items (10)

Solvable points on smooth projective varieties ⋮ Weil–Châtelet divisible elements in Tate–Shafarevich groups I: The Bashmakov problem for elliptic curves over ⋮ Supersingular elliptic curves over \(\mathbb{Z}_p\)-extensions ⋮ Selmer Groups and AnticyclotomicZ_p-extensions ⋮ The \(p\)-adic Gross-Zagier formula for elliptic curves at supersingular primes ⋮ Solvable points on genus-one curves over local fields ⋮ Fine Selmer groups, Heegner points and anticyclotomic ℤp-extensions ⋮ Tate–Shafarevich groups in anticyclotomic ℤ_p-extensions at supersingular primes ⋮ Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes ⋮ Kolyvagin's work and anticyclotomic tower fields: the supersingular case

Cites Work

• Heegner points and derivatives of \(L\)-series
• Sur les coefficients de Fourier des formes modulaires de poids demi-entier
• Mean values of derivatives of modular \(L\)-series
• On the structure of Selmer groups
• Iwasawa theory for elliptic curves at supersingular primes
• Mazur's conjecture on higher Heegner points.
• Special values of anticyclotomic \(L\)-functions.
• Galois representations.
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Galois properties of points of finite order of elliptic curves
• Nonvanishing theorems for L-functions of modular forms and their derivatives
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Iwasawa theory of elliptic curves at supersingular primes over ℤ p -extensions of number fields
• Kolyvagin's descent and Mordell-Weil groups over ring class fields.
• Fonctions $L$ $p$-adiques, théorie d'Iwasawa et points de Heegner
• Kolyvagin systems
• Solvable Points on Projective Algebraic Curves
• Integration on \({\mathcal H_p}\times\mathcal H\) and arithmetic applications.
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Solvable points on genus one curves