Growth of torsion groups of elliptic curves upon base change from number fields

DOI10.1007/s11139-023-00766-6arXiv2210.16977OpenAlexW4385461185MaRDI QIDQ6144576

Tyler Genao

Publication date: 29 January 2024

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.16977

zbMATH Keywords

torsion subgroupelliptic curveGalois representationcomplex multiplication

Mathematics Subject Classification ID

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

Cites Work

• On the field of definition of \(p\)-torsion points on elliptic curves over the rationals
• Bounds for the torsion of elliptic curves over number fields
• Residual Galois representations of elliptic curves with image contained in the normaliser of a nonsplit Cartan
• Typically bounding torsion on elliptic curves with rational \(j\)-invariant
• Torsion points and Galois representations on CM elliptic curves
• Uniform boundedness in terms of ramification
• Galois properties of points of finite order of elliptic curves
• The Arithmetic of Elliptic Curves
• Torsion Subgroups of CM Elliptic Curves over Odd Degree Number Fields:
• Determinants of subquotients of Galois representations associated with abelian varieties
• Growth of torsion groups of elliptic curves upon base change
• On the surjectivity of mod ℓ$\ell$ representations associated to elliptic curves
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