Relating the Tate-Shafarevich group of an elliptic curve with the class group

DOI10.2140/pjm.2021.312.203zbMath1487.11057arXiv1912.12928OpenAlexW3196029733MaRDI QIDQ2046746

Dipendra Prasad, Sudhanshu Shekhar

Publication date: 19 August 2021

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

Full work available at URL: https://arxiv.org/abs/1912.12928

zbMATH Keywords

Galois cohomologyelliptic curveTate-Shafarevich groupclass groupSelmer group

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Related Items (3)

Asymptotic behavior of class groups and cyclotomic Iwasawa theory of elliptic curves ⋮ Ideal class groups of number fields and Bloch-Kato's Tate-Shafarevich groups for symmetric powers of elliptic curves ⋮ On the corank of the fine Selmer group of an elliptic curve over a \(\mathbb{Z}_p\)-extension

Cites Work

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• Eisenstein congruences for split reductive groups
• A modular construction of unramified p-extensions of \(\mathbb{Q}(\mu_p)\)
• Selmer groups and the Eisenstein-Klingen ideal.
• Visibility of Shafarevich-Tate groups of abelian varieties.
• Local torsion primes and the class numbers associated to an elliptic curve over \(\mathbb{Q}\)
• On the class numbers of the fields of the \(p^n\)-torsion points of certain elliptic curves over \(\mathbb{Q}\)
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Galois properties of points of finite order of elliptic curves
• Congruence Between a Siegel and an Elliptic Modular Form
• Néron Models
• Visualizing Elements in the Shafarevich—Tate Group

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