Galois representations attached to abelian varieties of CM type

DOI10.24033/bsmf.2745zbMath1390.14137arXiv1506.04734OpenAlexW2963323792MaRDI QIDQ4635079

Davide Lombardo

Publication date: 13 April 2018

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.04734

zbMATH Keywords

elliptic curvescomplex multiplicationGalois representationsMumford-Tate group

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Galois representations (11F80) Complex multiplication and abelian varieties (14K22)

Related Items (12)

How big is the image of the Galois representations attached to CM elliptic curves? ⋮ Non-isogenous abelian varieties sharing the same division fields ⋮ Entanglement in the family of division fields of elliptic curves with complex multiplication ⋮ Computing the geometric endomorphism ring of a genus-2 Jacobian ⋮ Galois representations attached to elliptic curves with complex multiplication ⋮ Torsion points on isogenous abelian varieties ⋮ -adic images of Galois for elliptic curves over (and an appendix with John Voight) ⋮ Towards a classification of entanglements of Galois representations attached to elliptic curves ⋮ On the local-global principle for isogenies of abelian surfaces ⋮ Torsion points and isogenies on CM elliptic curves ⋮ Torsion points and Galois representations on CM elliptic curves ⋮ Some uniform bounds for elliptic curves over \(\mathbb{Q} \)

Cites Work

• Lower bounds for the ranks of CM types
• Additive reduction of algebraic tori
• On Galois representations for abelian varieties with complex and real multiplications.
• Good reduction of abelian varieties
• Algebraic cycles on abelian varieties of complex multiplication type
• Galois properties of points of finite order of elliptic curves
• Arithmetic of algebraic tori
• Points de torsion sur les variétés abéliennes de type GSp
• Brauer-Siegel for arithmetic tori and lower bounds for Galois orbits of special points
• The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point
• On the Field Extension by Complex Multiplication
• Profinite Groups, Arithmetic, and Geometry. (AM-67)
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