Congruences between Selmer groups

DOI10.1006/jnth.1999.2445zbMath1029.11029arXivmath/9809212OpenAlexW2019347316MaRDI QIDQ1969349

Li Guo

Publication date: 9 February 2004

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

Full work available at URL: https://arxiv.org/abs/math/9809212

zbMATH Keywords

Abelian groupsmodular formsBloch-Kato conjectureBernoulli numbersspecial valuesHecke characterscongruences between Galois representationscongruences of Selmer groupscyclotomic representations

Mathematics Subject Classification ID

Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Iwasawa theory (11R23) Galois cohomology (11R34)

Uses Software

• ecdata

Cites Work

• \(p\)-adic \(L\)-functions for CM fields
• Class fields of abelian extensions of \(\mathbb Q\)
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• General Selmer groups and critical values of Hecke \(L\)-functions
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• Modular elliptic curves and Fermat's Last Theorem
• On the Bloch-Kato conjecture for Hecke \(L\)-functions
• A generalisation of the Cassel-Tate pairing.
• Construction de représentations $p$-adiques
• The Bloch-Kato conjecture for adjoint motives of modular forms
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