The continuous cohomology of period domains over local fields

2005/05/19 by Sascha Orlik, Orlik, Sascha
Mathematics · #14G22 #14L05 #14L24 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #math.AG #math.NT #msc:14G22 #msc:14L05 #msc:14L24

paper · pdf · doi:10.48550/arxiv.math/0505409

16 pages, LaTeX

arxiv created 2005/05/19 · openalex publication_date 2005/05/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 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.

Citations

• A comparison theorem for l-adic cohomology
• On Extensions of generalized Steinberg Representations

Related

• The cohomology of period domains for reductive groups over finite fields
• On the sheaf cohomology of some p-adic period domains with coefficients in certain line bundles
• On the structure of some p-adic period domains
• On the cohomology of tori over local fields with perfect residue field
• Period-index problems in WC-groups IV: a local transition theorem