Elliptic surfaces over ℙ1 and large class groups of number fields

DOI10.1142/S1793042119501185zbMath1439.11279arXiv1811.08166MaRDI QIDQ4971997

Aaron Levin, Jean Gillibert

Publication date: 22 November 2019

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.08166

zbMATH Keywords

elliptic surfacesideal class groups

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic surfaces, elliptic or Calabi-Yau fibrations (14J27) Class numbers, class groups, discriminants (11R29)

Related Items (4)

Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil rank ⋮ Hilbert’s Irreducibility Theorem andideal class groups of quadratic fields ⋮ On the \(p\)-ranks of the ideal class groups of imaginary quadratic fields ⋮ Quadratic fields with a class group of large 3-rank

Cites Work

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• Pulling back torsion line bundles to ideal classes
• Ideal class groups, Hilbert's irreducibility theorem, and integral points of bounded degree on curves
• Construction of pure cubic fields with large 2-class groups
• Elliptic curves with large rank over function fields
• Chevalley-Weil theorem and subgroups of class groups
• Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil rank
• Ramification and class towers of number fields
• On unramified Galois extensions of quadratic number fields
• Néron Models
• An explicit family of cubic number fields with large 2-rank of the class group
• Selmer groups and class groups
• A Class Rank Estimate for Algebraic Number Fields
• On an elliptic curve over \(\mathbb{Q} (t)\) of rank \(\geq 14\)

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