Some uniform bounds for elliptic curves over \(\mathbb{Q} \)

DOI10.2140/pjm.2022.320.133OpenAlexW4306353698MaRDI QIDQ2090290

Sebastiano Tronto, Davide Lombardo

Publication date: 25 October 2022

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

Full work available at URL: https://arxiv.org/abs/2106.09950

zbMATH Keywords

elliptic curvesKummer theoryGalois representationsdivision points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Galois representations (11F80) Arithmetic ground fields for abelian varieties (14K15)

Uses Software

• ecdata

Cites Work

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• Tetrahedral elliptic curves and the local-global principle for isogenies
• Uniform bounds for homotheties in the Galois image associated with elliptic curves
• Serre's uniformity problem in the split Cartan case
• Bounds for Serre's open image theorem for elliptic curves over number fields
• On uniform lower bound of the Galois images associated to elliptic curves
• Autour d'une conjecture de Serge Lang. (Around a conjecture by Serge Lang)
• Kummer theory on extensions of Abelian varieties by tori
• On the number of Q-isomorphism classes of elliptic curves in each Q- isogeny class
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Modular curves and the Eisenstein ideal
• Galois theory and torsion points on curves.
• Galois cohomology and class field theory. Translated from the French by Andrei Yafaev
• The 1-eigenspace for matrices in \(\mathrm{GL}_{2}(\mathbb Z_{\ell})\)
• Elliptic curves over \(\mathbb {Q}\) and 2-adic images of Galois
• Residual Galois representations of elliptic curves with image contained in the normaliser of a nonsplit Cartan
• Galois representations attached to elliptic curves with complex multiplication
• Torsion points and Galois representations on CM elliptic curves
• Explicit Chabauty-Kim for the split Cartan modular curve of level 13
• An application of the division theory of elliptic functions to diophantine approximation
• Galois properties of points of finite order of elliptic curves
• The image of Galois representations attached to elliptic curves with an isogeny
• Almost all elliptic curves are Serre curves
• Galois theory of iterated endomorphisms
• The Arithmetic of Elliptic Curves
• Galois representations attached to abelian varieties of CM type
• Effective Kummer Theory for Elliptic Curves
• -adic images of Galois for elliptic curves over (and an appendix with John Voight)
• Torsion points and isogenies on CM elliptic curves
• Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves
• Determinants of subquotients of Galois representations associated with abelian varieties
• Vanishing of Some Galois Cohomology Groups for Elliptic Curves
• Composite images of Galois for elliptic curves over $\mathbf {Q}$ and entanglement fields
• On elliptic curves with an isogeny of degree 7
• REDUCTIONS OF POINTS ON ALGEBRAIC GROUPS, II
• Number Theory

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