The work described here began as an attempt to understand the structure of the cohomology groups associated to a subgroup ? of nite index of SL 2 (Z) which are not congruence subgroups. One knows that to the space of cusp forms of weight w > 2 on ? (whose dimension we denote by d) one can 15] attach a motive M, which is pure of weight w?1 and of rank 2d, deened over some number eld; it is a dir...

— It is shown here that, for any finitely generated lattice r in certain semi simple groups over local fields of positive characteristics, H (r. Ad) is nonvanishing; this is in sharp contrast with the situation in characteristic zero. Let Kbe a local field (i. e. a non-discrete locally compact field), and let G be a connected semi simple algebraic group defined over K. Let G = G (K), and let r ...