2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75247In this paper we consider period domains over local fields for quasi-split reductive groups. We compute the continuous l-adic cohomology with compact support of them in the case of a basic isocrystal. This paper is a continuation of [O2] where we considered the etale cohomology with torsion coefficients of these spaces.16 pages, LaTeXNumber TheoryAlgebraic Geometry14L05; 14G22, 14L24text