Torsion points and Galois representations on CM elliptic curves

DOI10.2140/pjm.2020.305.43zbMath1480.11070arXiv1612.03229OpenAlexW3011239213MaRDI QIDQ2306071

Abbey Bourdon, Pete L. Clark

Publication date: 20 March 2020

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.03229

zbMATH Keywords

elliptic curvescomplex multiplicationGalois representationstorsion points

Mathematics Subject Classification ID

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

Related Items (19)

How big is the image of the Galois representations attached to CM elliptic curves? ⋮ Torsion for CM elliptic curves defined over number fields of degree 2𝑝 ⋮ Entanglement in the family of division fields of elliptic curves with complex multiplication ⋮ Typically bounding torsion on elliptic curves with rational \(j\)-invariant ⋮ Galois representations attached to elliptic curves with complex multiplication ⋮ Torsion points on isogenous abelian varieties ⋮ An Algorithm for Determining Torsion Growth of Elliptic Curves ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ On somep‐adic Galois representations and form class groups ⋮ Growth of torsion groups of elliptic curves upon base change from number fields ⋮ Towards a classification of entanglements of Galois representations attached to elliptic curves ⋮ The least degree of a CM point on a modular curve ⋮ Odd degree isolated points on \(X_1(N)\) with rational \(j\)-invariant ⋮ The torsion subgroup of a family of elliptic curves over the maximal abelian extension of $\mathbb{Q}$ ⋮ Torsion points and isogenies on CM elliptic curves ⋮ Acyclotomy of torsion in the CM case ⋮ Cartan images and \(\ell \)-torsion points of elliptic curves with rational \(j\)-invariant ⋮ Some uniform bounds for elliptic curves over \(\mathbb{Q} \) ⋮ On the level of modular curves that give rise to isolated \(j\)-invariants

Cites Work

• Anatomy of torsion in the CM case
• Rational torsion in complex-multiplication elliptic curves
• Torsion bounds for elliptic curves and Drinfeld modules
• Complete classification of torsion of elliptic curves over quadratic cyclotomic fields
• Points of finite order on elliptic curves with complex multiplication
• Uniform boundedness in terms of ramification
• The truth about torsion in the CM case
• Galois properties of points of finite order of elliptic curves
• Computation on elliptic curves with complex multiplication
• Minimal Torsion in Isogeny Classes of Elliptic Curves
• Torsion Subgroups of CM Elliptic Curves over Odd Degree Number Fields:
• Galois representations attached to abelian varieties of CM type
• Torsion des variétés abéliennes CM
• Die Teilwerte der Weberschen Tau-Funktion.
• TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE)
• Advanced Topics in Computional Number Theory
• Torsion points on CM elliptic curves over real number fields
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Torsion points and Galois representations on CM elliptic curves