Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results

DOI10.1215/00127094-2009-010zbMath1177.11050arXiv0706.0566OpenAlexW3102877948WikidataQ124843479 ScholiaQ124843479MaRDI QIDQ1006537

Bjorn Poonen, Alexandru Buium

Publication date: 25 March 2009

Published in: Duke Mathematical Journal, Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0706.0566

zbMATH Keywords

reciprocity lawabelian varietiesShimura curvemodular curveElliptic curvesCM pointscanonical liftCM pointarithmetic differential equation

Mathematics Subject Classification ID

Local ground fields in algebraic geometry (14G20) Arithmetic aspects of modular and Shimura varieties (11G18) Modular and Shimura varieties (14G35) Global ground fields in algebraic geometry (14G25)

Related Items (19)

Independence of CM points in elliptic curves ⋮ Differential modular forms on Shimura curves over totally real fields ⋮ On a conjecture of Buium and Poonen ⋮ Canonical Witt formal scheme extensions and \(p\)-torsion groups ⋮ The ring of differential Fourier expansions ⋮ Hecke operators on differential modular forms mod \(p\) ⋮ Arithmetic jet spaces ⋮ \(o\)-minimality and the André-Oort conjecture for \(\mathbb{C}^{n}\) ⋮ Solutions to arithmetic differential equations in algebraically closed fields ⋮ The basic geometry of Witt vectors. II: Spaces ⋮ Arithmetic Levi-Cività connection ⋮ The Euler top and canonical lifts ⋮ Arithmetic differential equations in several variables ⋮ Sur le rang des courbes elliptiques sur les corps de classes de Hilbert ⋮ Differential modular forms over totally real fields of integral weights ⋮ Unlikely intersections between isogeny orbits and curves ⋮ Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results ⋮ Differential modular forms attached to newforms mod \(p\) ⋮ Perfectoid spaces arising from arithmetic jet spaces

Cites Work

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• Independence of points on elliptic curves arising from special points on modular and Shimura curves. I: Global results
• Finiteness theorems for abelian varieties over number fields.
• Heegner points and derivatives of \(L\)-series
• Hyperbolic distribution problems and half-integral weight Maass forms
• Heegner points and derivatives of \(L\)-series. II
• Wieferich's criterion and the abc-conjecture
• Mordell-Lang plus Bogomolov
• Integral models of certain Shimura curves
• Distribution of almost division points
• Uniform distribution of Heegner points.
• Mazur's conjecture on higher Heegner points.
• Hecke points on modular curves
• A tameness criterion for Galois representations associated to modular forms (mod \(p\))
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Differential characters of abelian varieties over \(p\)-adic fields
• Elliptic Wieferich primes
• On the independence of Heegner points associated to distinct quadratic imaginary fields
• Galois properties of points of finite order of elliptic curves
• Rational points of Abelian varieties with values in towers of number fields
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• A Combination of the Conjectures of Mordell-Lang and André-Oort
• FINITENESS OF $ E(\mathbf{Q})$ AND $ \textrm{Ø}(E,\mathbf{Q})$ FOR A SUBCLASS OF WEIL CURVES
• A Note on Manin's Theorem of the Kernel
• Differential Modular Forms on Shimura Curves, I
• Hauteur des correspondances de Hecke
• Heights of Heegner points on Shimura curves.

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