**Papers Published**

- Saper, L,
*ℒ-modules and the conjecture of Rapoport and Goresky-Macpherson*, in Formes Automorphes (I) — Actes du Semestre du Centre Émile Borel, printemps 2000, edited by Tilouine, J; Carayol, H; Harris, M; Vignéras, M-F, vol. 298 no. 298 (2005), pp. 319-334, ISSN 0303-1179, ISBN 2-85629-172-4

(last updated on 2020/04/04)**Abstract:**

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.