On the Eisenstein cohomology of arithmetic groups

DOI10.1215/S0012-7094-04-12315-2zbMath1057.11031OpenAlexW1963734409MaRDI QIDQ1885556

Jian-Shu Li, Joachim Schwermer

Publication date: 11 November 2004

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-04-12315-2

zbMATH Keywords

harmonic analysisEisenstein cohomology

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Cohomology of arithmetic groups (11F75)

Related Items

Vanishing theorems for coherent automorphic cohomology ⋮ Picard modular forms and the cohomology of local systems on a Picard modular surface ⋮ Algèbres de Hecke quasi-ordinaires universelles ⋮ Universal eigenvarieties, trianguline Galois representations, and \(p\)-adic Langlands functoriality ⋮ Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties ⋮ Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties ⋮ De Rham comparison and Poincaré duality for rigid varieties ⋮ Eisenstein cohomology for congruence subgroups of \(\text{SO}(n,2)\) ⋮ Rational structures on automorphic representations ⋮ WHITTAKER PERIODS, MOTIVIC PERIODS, AND SPECIAL VALUES OF TENSOR PRODUCT -FUNCTIONS ⋮ Eisenstein series for rank one unitary groups and some cohomological applications ⋮ Eigenvarieties for reductive groups ⋮ Geometric cycles, Albert algebras and related cohomology classes for arithmetic groups ⋮ Parabolic eigenvarieties via overconvergent cohomology ⋮ Geometric cycles, arithmetic groups and their cohomology ⋮ Coherent cohomology and Galois representations ⋮ Low degree cohomologies of congruence groups ⋮ On Eisenstein series and the cohomology of arithmetic groups ⋮ Borel's stable range for the cohomology of arithmetic groups ⋮ Inner cohomology of \(\mathrm{GL}_n\) ⋮ Eisenstein series and the top degree cohomology of arithmetic subgroups of \(\operatorname{SL}_n/\mathbb{Q} \) ⋮ Eisenstein Cohomology and Automorphic L-Functions ⋮ On mixed Hodge structures of Shimura varieties attached to inner forms of the symplectic group of degree two ⋮ On the boundary and intersection motives of genus 2 Hilbert-Siegel varieties ⋮ On some arithmetic properties of automorphic forms ofGL_mover a division algebra ⋮ Characteristic classes of bundles of \(K3\) manifolds and the Nielsen realization problem ⋮ Residues of Eisenstein series and the automorphic cohomology of reductive groups ⋮ Equidimensional adic eigenvarieties for groups with discrete series ⋮ The residual Eisenstein cohomology of $Sp_{4}$ over a totally real number field ⋮ A construction of residues of Eisenstein series and related square-integrable classes in the cohomology of arithmetic groups of low \(k\)-rank

Cites Work

• Regularization theorems in Lie algebra cohomology. Applications
• On liftings and cusp cohomology of arithmetic groups
• Eisenstein cohomology of arithmetic groups. The case \(GL_ 2\)
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• On the functional equations satisfied by Eisenstein series
• A decomposition of spaces of automorphic forms, and the Eisenstein cohomology of arithmetic groups
• Eisenstein series and cohomology of arithmetic groups: The generic case
• Unitary representations of Gl(n,R) with non-trivial (g,K)-cohomology
• Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen
• Lie algebra cohomology and the generalized Borel-Weil theorem
• Automorphic forms on semisimple Lie groups. Notes by J. G. M. Mars.
• Holomorphy of Eisenstein series at special points and cohomology of arithmetic subgroups of SLn (Q).
• On Euler products and residual Eisenstein cohomology classes for Siegel modular varieties
• Harmonic analysis in weighted L2-spaces
• Projective limits of locally symmetric spaces and cohomology.
• Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item