The cohomology of arithmetic groups is made up of two pieces, the cuspidal and noncuspidal parts. Within the cuspidal cohomology is a subspace— the /-cuspidal cohomology—spanned by the classes that generate representations of the associated finite Lie group which are cuspidal in the sense of finite Lie group theory. Few concrete examples of /-cuspidal cohomology have been computed geometrically...

Let $G = {rm Res}_{F/mathbb{Q}}(GL_n)$ where $F$ is a number field‎. ‎Let $S^G_{K_f}$ denote an ad`elic locally symmetric space for some level structure $K_f.$ Let ${mathcal M}_{mu,{mathbb C}}$ be an algebraic irreducible representation of $G({mathbb R})$ and we let $widetilde{mathcal{M}}_{mu,{mathbb C}}$ denote the associated sheaf on $S^G_{K_f}.$ The aim of this paper is to classify the data ...

Let F be a real quadratic field with ring of integers Ø and with class number 1. Let Γ be a congruence subgroup of GL2(Ø). We describe a technique to compute the action of the Hecke operators on the cohomology H(Γ ;C). For F real quadratic this cohomology group contains the cuspidal cohomology corresponding to cuspidal Hilbert modular forms of parallel weight 2. Hence this technique gives a way...

In a previous paper [Avner Ash, Paul E. Gunnells, Mark McConnell, Cohomology of congruence subgroups of SL4(Z), J. Number Theory 94 (2002) 181–212] we computed cohomology groups H (Γ0(N),C), where Γ0(N) is a certain congruence subgroup of SL(4,Z), for a range of levels N . In this note we update this earlier work by extending the range of levels and describe cuspidal cohomology classes and addi...

The cuspidal cohomology groups of arithmetic groups in certain infinite dimensional Modules are computed. As a result we get a simultaneous generalization of the Patterson-Conjecture and the Lewis-Correspondence. 2000 Mathematics Subject Classification: 11F75

We conjecture that the only irreducible cuspidal automorphic representations for GL(3)/Q of cohomological type and level 1 are (up to twisting) the symmetric square lifts of classical cuspforms on GL(2)/Q of level 1. We present computational evidence for this conjecture. 1. Statement and explanation of a conjecture Arithmetic objects defined over Q and unramified everywhere are rare. For exampl...

Let $G$ be a reductive group over number field $F$, which is split at finite place $\mathfrak{p}$ of and let $\pi$ cuspidal automorphic representation $G$, cohomological with respect to the trivial coefficient system Steinberg $\mathfrak{p}$. We use cohomology $\mathfrak{p}$-arithmetic subgroups attach $\mathcal{L}$-invariants $\pi$. This generalizes construction Darmon (respectively Spie\ss), ...

Conjectures concerning the relations between motives and automorphic representations of GL(n) over number elds have been made by Clozel C1]. They make precise part of the programme indicated by Langlands in La]. Once a motive is attached to an automorphic representation, one can derive a compatible series of-adic representations of Gal(Q=Q) attached to it in the usual way. In C2], Clozel has gi...