On Extensions of generalized Steinberg Representations

Let F be a local non-archimedean field and let G be the group of F-valued points of a reductive algebraic group over F. In this paper we compute the Ext-groups of generalized Steinberg representations in the category of smooth G-representations with coefficients in a certain self-injective ring.Comment: 22 pages, LaTe

The cohomology of period domains for reductive groups over finite fields

ABSTRACT. – The goal of this paper is to give an explicit formula for the -adic cohomology of period domains over finite fields for arbitrary reductive groups. The result is a generalisation of the computation in [6] which treats the case of the general linear group GLn. 2001 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – Dans cet article, nous donnons une formule explicite pour la cohomologie des domaines de périodes sur un corps fini dans le cas d’un groupe réductif quelconque. Le résultat est une généralisatio