2001/12/31 by Leslie Saper
Mathematics · #math.RT #math.DG #msc:11F75 #msc:22E40 #msc:32S60 #msc:55N33 #msc:14G35 #msc:22E45
published as Formes Automorphes (I) -- Actes du Semestre du Centre Émile Borel, printemps 2000 (J. Tilouine, H. Carayol, M. Harris, and M.-F. Vignéras, eds.), Astérisque 298 (2005), pp. 319-334 · 16 pages, 4 figures, AMS-LaTeX, smfart.cls, uses xypic 3.7 package; v2: minor typos fixed, definitions of D_P(V) and n_P(V) corrected; v3: various references added in footnotes; v4: updated bibliography, revised and translated abstract, minor typos fixed
arxiv created 2005/05/13 · arxiv updated 2009/11/30
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-modules 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 (math.RT/0112251). 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.