Adjoint modular Galois representations and their Selmer groups

DOI10.1073/pnas.94.21.11121zbMath0909.11025OpenAlexW2029720726WikidataQ36256392 ScholiaQ36256392MaRDI QIDQ4372150

Jacques Tilouine, Haruzo Hida, Eric Urban

Publication date: 21 January 1998

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.94.21.11121

zbMATH Keywords

Galois representationSelmer groupsclass number formulas\(p\)-adic \(L\)-functionadjoint representationmodular elliptic curve

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items

How can we construct abelian Galois extensions of basic number fields?, On the search of genuine $p$-adic modular $L$-functions for $GL(n)$. With a correction to: On $p$-adic $L$-functions of $GL(2)\times{}GL(2)$ over totally real fields, Adjoint Selmer groups as Iwasawa modules, Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations, Selmer groups and the Eisenstein-Klingen ideal.

Cites Work

• On the anticyclotomic main conjecture
• Congruences of cusp forms and special values of their zeta functions
• Galois representations, Kähler differentials and ``main conjectures
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• On the anticyclotomic main conjecture for CM fields
• A finiteness theorem for the symmetric square of an elliptic curve
• A proof of the Mahler-Manin conjecture
• The Iwasawa conjecture for totally real fields
• Modules of Congruence of Hecke Algebras and L-Functions Associated with Cusp Forms