The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication

DOI10.1215/21562261-2017-0018zbMath1442.11145arXiv1507.07309OpenAlexW1001638561WikidataQ123199674 ScholiaQ123199674MaRDI QIDQ1753062

Xianqiang Yang

Publication date: 25 May 2018

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

Full work available at URL: https://arxiv.org/abs/1507.07309

zbMATH Keywords

Selmer groupscomplex multiplicationHilbert modular forms\(p\)-adic \(L\)-functionsIwasawa main conjecture

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) 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 (3)

Height one specializations of Selmer groups ⋮ Specialization method in Krull dimension two and Euler system theory over normal deformation rings ⋮ On the Brumer-Stark conjecture

Cites Work

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• Surjectivity of the global-to-local map defining a Selmer group
• \(p\)-adic \(L\)-functions for CM fields
• Class fields of abelian extensions of \(\mathbb Q\)
• On \(p\)-adic analogues of the conjectures of Birch and Swinnerton-Dyer
• On Galois representations associated to Hilbert modular forms
• On \(L\)-functions of elliptic curves and cyclotomic towers
• On \(p\)-adic representations for totally real fields
• Modular forms in characteristic \(\ell\) and special values of their \(L\)-functions
• L-functions and division towers
• On p-adic Hecke algebras for \(GL_ 2\) over totally real fields
• On ordinary \(\lambda\)-adic representations associated to modular forms
• The ``main conjectures of Iwasawa theory for imaginary quadratic fields
• Periods of Hecke characters
• The special values of the zeta functions associated with Hilbert modular forms
• On the structure of certain Galois groups
• Motives for Hilbert modular forms
• On the anticyclotomic main conjecture for CM fields
• Motives over totally real fields and \(p\)-adic \(L\)-functions
• \(p\)-adic \(L\)-functions of Hilbert modular forms
• Fine Selmer groups of elliptic curves over \(p\)-adic Lie extensions
• Euler system for Galois deformations.
• Several variables \(p\)-adic \(L\)-functions for Hida families of Hilbert modular forms
• On the structure of certain Galois cohomology groups
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• On automorphic forms on \(mathrm{GL}_2\) and Hecke operators
• Automorphic symbols, <i>p</i>-adic <i>L</i>-functions and ordinary cohomology of Hilbert modular varieties
• Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields
• Cohomologie d'intersection et fonctions $L$ de certaines variétés de Shimura
• The exceptional zero conjecture for Hilbert modular forms
• The Cuspidal Group and Special Values of L-Functions
• L-Indistinguishability For SL (2)
• On the Iwasawa Invariants of Totally Real Number Fields
• NON-ARCHIMEDEAN INTEGRATION AND JACQUET-LANGLANDSp-ADICL-FUNCTIONS
• Sur les représentations $l$-adiques associées aux formes modulaires de Hilbert
• Euler Systems
• On the Structure of Selmer Groups
• Anti-cyclotomic Katz $p$-adic $L$-functions and congruence modules
• On the critical values of Hecke L-series

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