Control theorems of $p$-nearly ordinary cohomology groups for $\text {SL} (n)$

DOI10.24033/bsmf.2266zbMath0852.11023OpenAlexW268891517MaRDI QIDQ4869988

Haruzo Hida

Publication date: 5 December 1996

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1995__123_3_425_0

zbMATH Keywords

Borel subgroupscontrol theorems\(p\)-adic cohomological modular forms\(p\)-adic nearly ordinary cohomology groups\(p\)-adic nearly ordinary Hecke algebrasindependence of weight

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (p)-adic theory, local fields (11F85) Cohomology of arithmetic groups (11F75)

Related Items (17)

Estimées pour les valuations $p$-adiques des valeurs propres des opérateurs de Hecke ⋮ \(p\)-adic \(L\)-functions of Hilbert cusp forms and the trivial zero conjecture ⋮ Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields ⋮ Algèbres de Hecke quasi-ordinaires universelles ⋮ Universal eigenvarieties, trianguline Galois representations, and \(p\)-adic Langlands functoriality ⋮ Modularity lifting theorems for ordinary Galois representations ⋮ Purity for families of Galois representations ⋮ Growth of Hecke Fields Along a p-Adic Analytic Family of Modular Forms ⋮ Derived Hecke action at p and the ordinary p -adic cohomology of arithmetic manifolds ⋮ P-adic L-functions in universal deformation families ⋮ Eigenvarieties for reductive groups ⋮ Congruence module for \(\text{GL}(2)\) of an imaginary quadratic field and Iwasawa theory of biquadratic CM field ⋮ L-functions of GL_2n: p-adic properties and non-vanishing of twists ⋮ Conductors in \(p\)-adic families ⋮ Transcendence of Hecke operators in the big Hecke algebra ⋮ Familles de formes modulaires de Drinfeld pour le groupe général linéaire ⋮ Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

Cites Work

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• On p-adic Hecke algebras for \(GL_ 2\) over totally real fields
• Représentations galoisiennes associées aux représentations automorphes autoduales de \(GL(n)\). (Galois representations associated with self-dual automorphic representations of \(GL(n)\))
• \(p\)-ordinary cohomology groups for \(\text{SL}(2)\) over number fields
• On the cohomology of Kottwitz's arithmetic varieties
• \(p\)-adic Hecke algebras for \(GL(2)\)
• Corners and arithmetic groups (Appendice: Arrondissement des varietes a coins par A. Douady et L. Herault)
• On vector bundle valued harmonic forms and automorphic forms on symmetric Riemannian manifolds
• Le spectre résiduel de ${\rm GL}(n)$
• Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula. (AM-120)
• Modular 𝑝-adic 𝐿-functions and 𝑝-adic Hecke algebras
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