ℒ-modules and the conjecture of Rapoport and Goresky-Macpherson

Book Section (Chapter)

Consider the middle perversity intersection cohomology groups of various compactifications of a Hermitian locally symmetric space. Rapoport and independently Goresky and MacPherson have conjectured that these groups coincide for the reductive Borel-Serre compactification and the Baily-Borel-Satake compactification. This paper describes the theory of ℒ-modulcs and how it is used to solve the conjecture. More generally we consider a Satake compactification for which all real boundary components are equal-rank. Details will be given elsewhere, As another application of ℒ-modules, we prove a vanishing theorem for the ordinary cohomology of a locally symmetric space. This answers a question raised by Tilouine.

Full Text

Duke Authors

Cited Authors

  • Saper, L

Cited Editors

  • Tilouine, J; Carayol, H; Harris, M; Vignéras, M-F

Published Date

  • 2005

Volume / Issue

  • 298 /

Book Title

  • Formes Automorphes (I) — Actes du Semestre du Centre Émile Borel, printemps 2000

Start / End Page

  • 319 - 334

International Standard Book Number 10 (ISBN-10)

  • 2-85629-172-4