scientific article; zbMATH DE number 5036535

zbMath1142.11036MaRDI QIDQ5475900

Jacques Tilouine, Alain Genestier

Publication date: 27 June 2006

Full work available at URL: http://smf4.emath.fr/en/Publications/Asterisque/2005/302/html/smf_ast_302_177-290.html

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zbMATH Keywords

vanishing cyclesbad reductionGalois representationsSiegel modular formsSiegel varietiesparahoric levelEichler-Shimura relations

Mathematics Subject Classification ID

Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18) Langlands-Weil conjectures, nonabelian class field theory (11R39) Modular correspondences, etc. (11F32) Galois cohomology (11R34)

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Integral period relations and congruences ⋮ Minimal modularity lifting for nonregular symplectic representations ⋮ Deformation Theory and Local-Global Compatibility of Langlands Correspondences ⋮ Yoshida lifts and Selmer groups ⋮ Nearby cycles of automorphic étale sheaves ⋮ Companion forms for unitary and symplectic groups ⋮ Reciprocity in the Langlands program since Fermat's last theorem ⋮ Proof of de Smit’s conjecture: a freeness criterion ⋮ SYMMETRIC POWER CONGRUENCE IDEALS AND SELMER GROUPS ⋮ Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale ⋮ \(p\)-adic properties of motivic fundamental lines ⋮ Companion forms and the dual BGG complex for \(\mathrm{GSp}_4\) ⋮ A pairing on the cuspidal eigenvariety for \(\text{GSp}_{2g}\) and the ramification locus ⋮ Nearby Cycles of Automorphic Étale Sheaves, II ⋮ \(\mathcal L\)-invariant of symmetric powers of Tate curves ⋮ Good and semi-stable reductions of Shimura varieties ⋮ Galois level and congruence ideal for -adic families of finite slope Siegel modular forms ⋮ Abelian surfaces over totally real fields are potentially modular ⋮ Higher Hida theory and \(p\)-adic \(L\)-functions for \(\mathrm{GSp}_4\) ⋮ Higher coherent cohomology and \(p\)-adic modular forms of singular weights

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