Ideal class groups of number fields and Bloch-Kato's Tate-Shafarevich groups for symmetric powers of elliptic curves

DOI10.3836/tjm/1502179361OpenAlexW4285178649MaRDI QIDQ2683799

Naoto Dainobu

Publication date: 15 February 2023

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

Full work available at URL: https://arxiv.org/abs/2204.07759

zbMATH Keywords

elliptic curveideal class groupBloch-Kato's Selmer group

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Class numbers, class groups, discriminants (11R29) Galois cohomology (11R34)

Cites Work

• Class numbers of quadratic fields and Shimura's correspondence
• Iwasawa theory for elliptic curves at supersingular primes
• Relating the Tate-Shafarevich group of an elliptic curve with the class group
• A mod-\(p\) Artin-Tate conjecture, and generalizing the Herbrand-Ribet theorem
• Division fields of elliptic curves with minimal ramification
• Class Numbers of the Simplest Cubic Fields
• Euler Systems
• On the symplectic type of isomorphisms of the 𝑝-torsion of elliptic curves
• Vanishing of Some Galois Cohomology Groups for Elliptic Curves
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