Growth of in towers for isogenous curves

DOI10.1112/S0010437X15007423zbMath1351.11035arXiv1301.4257OpenAlexW2105290889MaRDI QIDQ3463481

Tim Dokchitser, Vladimir Dokchitser

Publication date: 14 January 2016

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4257

zbMATH Keywords

elliptic curvesabelian varietiesisogenyTate-Shafarevich groupSelmer group\(\mu\)-invariant\(p\)-adic Lie extensions

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Abelian varieties of dimension (> 1) (11G10) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Rational numbers as sums of fractions (11D68) Elliptic curves over local fields (11G07)

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Cites Work

• On Néron's classification of elliptic curves of residue characteristics 2 and 3
• On the Birch-Swinnerton-Dyer quotients modulo squares
• On the failure of semistability of elliptic curves with additive reduction
• The non-p-part of the class number in a cyclotomic \(\mathbb{Z}_p\)-extension
• The Magma algebra system. I: The user language
• On the Tate-Shafarevich groups over cyclotomic fields of an elliptic curve with supersingular reduction. I.
• Iwasawa \(\mu\)-invariants of elliptic curves and their symmetric powers.
• The \(\text{GL}_2\) main conjecture for elliptic curves without complex multiplication
• Galois properties of points of finite order of elliptic curves
• Ramification in p-adic Lie extensions
• A remark on Tate's algorithm and Kodaira types
• Computations in non-commutative Iwasawa theory
• Fonctions $L$ $p$-adiques, théorie d'Iwasawa et points de Heegner
• Local invariants of isogenous elliptic curves

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