Eisenstein cohomology and the construction of mixed motives

zbMath0795.11024MaRDI QIDQ1310794

Günter Harder

Publication date: 15 December 1993

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

zbMATH Keywords

cohomology groupsEisenstein seriesShimura varietiesautomorphic \(L\)-functionsintertwining operatorsEuler productsmixed motivesrelative Lie algebra cohomologycusp cohomologyconnected reductive algebraic groupEisenstein cohomology classesAnderson's mixed motivesBeilinson- Deligne conjecturesHecke algebra submodulesHodge-de Rham extension classtopological trace formula

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Galois representations (11F80) Arithmetic aspects of modular and Shimura varieties (11G18) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Modular and Shimura varieties (14G35) (Co)homology theory in algebraic geometry (14F99) Cohomology of arithmetic groups (11F75)

Related Items

Dirichlet motives via modular curves ⋮ On Eisenstein ideals and the cuspidal group of \(J_{0}(N)\) ⋮ A Simple Trace Formula for Algebraic Modular Forms ⋮ Picard modular forms and the cohomology of local systems on a Picard modular surface ⋮ Realisations of Kummer-Chern-Eisenstein-motives ⋮ Discrete series characters and the Lefschetz formula for Hecke operators ⋮ Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties ⋮ Siegel modular forms of degree three and the cohomology of local systems ⋮ Congruences to Ikeda-Miyawaki lifts and triple \(L\)-values of elliptic modular forms ⋮ Ghost classes in the cohomology of the Shimura variety associated to $GSp_4$ ⋮ On the cohomology of local systems on the moduli spaces of curves of genus 2 and of abelian surfaces. I ⋮ The Gorenstein conjecture fails for the tautological ring of \(\overline{\mathcal{M}}_{2,n}\) ⋮ Eigenvarieties for reductive groups ⋮ Congruence of Siegel modular forms and special values of their standard zeta functions ⋮ The Euler characteristic of local systems on the moduli of genus 3 hyperelliptic curves ⋮ Siegel Modular Forms and Their Applications ⋮ Equivariant Euler-Poincaré characteristic in sheaf cohomology ⋮ Denominators of Eisenstein cohomology classes for \(\text{GL}_2\) over imaginary quadratic fields ⋮ Eisenstein congruences for split reductive groups ⋮ Rank one Eisenstein cohomology of local systems on the moduli space of abelian varieties ⋮ CYCLIC ODD DEGREE BASE CHANGE LIFTING FOR UNITARY GROUPS IN THREE VARIABLES ⋮ Characters, genericity, and multiplicity one for \(U(3)\) ⋮ The residual Eisenstein cohomology of $Sp_{4}$ over a totally real number field