Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

DOI10.1016/S0012-9593(99)80021-4zbMath0991.11016OpenAlexW1968324480MaRDI QIDQ4719485

Jacques Tilouine, Eric Urban

Publication date: 24 January 2002

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1999_4_32_4_499_0

zbMATH Keywords

Galois representationBorel-Serre compactificationHida-Iwasawa algebranearly ordinary Hecke eigensystemsordinary cohomology groupordinary Hecke eigensystemseveral variable \(p\)-adic familySiegel cusp eigenform

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18) Iwasawa theory (11R23)

Related Items (24)

Euler systems for \(\mathrm{GSp}(4)\) ⋮ Families of Bianchi modular symbols: critical base-change \(p\)-adic \(L\)-functions and \(p\)-adic Artin formalism ⋮ On the Eisenstein cohomology of arithmetic groups ⋮ THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS ⋮ Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields ⋮ Algèbres de Hecke quasi-ordinaires universelles ⋮ Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties ⋮ On Siegel eigenvarieties at Saito-Kurokawa points ⋮ Modularity lifting theorems for ordinary Galois representations ⋮ SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS ⋮ The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\) ⋮ Two variable \(p\)-adic \(L\) functions attached to eigenfamilies of positive slope ⋮ Ordinary \(p\)-adic Eisenstein series and \(p\)-adic \(L\)-functions for unitary groups ⋮ -ADIC -FUNCTIONS FOR ORDINARY FAMILIES ON SYMPLECTIC GROUPS ⋮ Eigenvarieties for reductive groups ⋮ Congruence module for \(\text{GL}(2)\) of an imaginary quadratic field and Iwasawa theory of biquadratic CM field ⋮ Triple products of Coleman's families ⋮ On zeta functions and families of Siegel modular forms ⋮ Twisted adjoint \(L\)-values, dihedral congruence primes and the Bloch-Kato conjecture ⋮ Abelian surfaces over totally real fields are potentially modular ⋮ Selmer groups and the Eisenstein-Klingen ideal. ⋮ Iwasawa invariants of Galois deformations ⋮ On the \(p\)-adic deformations of Saito-Kurokawa lifts ⋮ On Greenberg’s L-invariant of the symmetric sixth power of an ordinary cusp form

Cites Work

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