On the anticyclotomic main conjecture for CM fields

DOI10.1007/BF01232236zbMath0819.11047OpenAlexW2061412972WikidataQ123183177 ScholiaQ123183177MaRDI QIDQ1328157

Haruzo Hida, Jacques Tilouine

Publication date: 31 August 1995

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/144210

zbMATH Keywords

Hilbert modular formsHecke algebraIwasawa main conjecturemain conjectureCM- fieldsHilbert-Blumenthal modular formsordinary Galois representations

Mathematics Subject Classification ID

Iwasawa theory (11R23) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (33)

Exterior powers in Iwasawa theory ⋮ Class groups and local indecomposability for non-CM forms ⋮ The Iwasawa main conjectures for \(\operatorname{GL}_2\) and derivatives of \(p\)-adic \(L\)-functions ⋮ Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules ⋮ THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS ⋮ Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields ⋮ On the non-critical exceptional zeros of Katz \(p\)-adic \(L\)-functions for CM fields ⋮ On local Galois representations associated to ordinary Hilbert modular forms ⋮ Explicit inner product formulas and Bessel period formulas for HST lifts ⋮ Iwasawa main conjecture for Rankin-Selberg \(p\)-adic \(L\)-functions ⋮ Height one specializations of Selmer groups ⋮ On the Iwasawa theory of CM fields for supersingular primes ⋮ Cohomology of normic systems and fake \(\mathbb{Z}_p\)-extensions ⋮ On the Iwasawa invariants of BDP Selmer groups and BDP \(p\)-adic \(L\)-functions ⋮ The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\) ⋮ The derivative formula of \(p\)-adic \(L\)-functions for imaginary quadratic fields at trivial zeros ⋮ Unnamed Item ⋮ 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 ⋮ Congruence module for \(\text{GL}(2)\) of an imaginary quadratic field and Iwasawa theory of biquadratic CM field ⋮ Geometry of the eigencurve at CM points and trivial zeros of Katz \(p\)-adic \(L\)-functions ⋮ Adjoint modular Galois representations and their Selmer groups ⋮ Anticyclotomic \(p\)-adic \(L\)-functions and Ichino's formula ⋮ The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication ⋮ Adjoint Selmer groups as Iwasawa modules ⋮ The algebraic functional equation of Selmer groups for CM fields ⋮ On \(p\)-adic L-functions of \(GL(2)\times GL(2)\) over totally real fields ⋮ Denominators of Eisenstein cohomology classes for \(\text{GL}_2\) over imaginary quadratic fields ⋮ On the Hilbert eigenvariety at exotic and CM classical weight 1 points ⋮ On \(p\)-adic \(L\)-functions of \(GL(2) \times{} GL(2)\) over totally real fields ⋮ Iwasawa theory for \(\mathrm{GL}_2\times \mathrm{Res}_{K/\mathbb{Q}}\mathrm{GL}_1\) ⋮ Big Galois representations and -adic -functions ⋮ Selmer groups and the Eisenstein-Klingen ideal. ⋮ Ordinary families of Klingen Eisenstein series on symplectic groups

Cites Work

• \(p\)-adic \(L\)-functions for CM fields
• Injective modules over Noetherian rings
• Class fields of abelian extensions of \(\mathbb Q\)
• On the anticyclotomic main conjecture
• On \(p\)-adic representations for totally real fields
• Growth of class numbers in \({\mathbb{Z}}_{\ell}\)-extensions connected with imaginary quadratic fields
• On p-adic Hecke algebras for \(GL_ 2\) over totally real fields
• On ordinary \(\lambda\)-adic representations associated to modular forms
• Galois representations, Kähler differentials and ``main conjectures
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• On the structure of certain Galois groups
• On \(p\)-adic L-functions of \(GL(2)\times GL(2)\) over totally real fields
• Local Euler characteristics
• On automorphic forms on \(mathrm{GL}_2\) and Hecke operators
• On some results of Atkin and Lehner
• Modules of Congruence of Hecke Algebras and L-Functions Associated with Cusp Forms
• Automorphic Forms on Adele Groups. (AM-83)
• Modular Forms and ℓ-Adic Representations
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
• Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
• Functors of Artin Rings
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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