L-modules and the Conjecture of Rapoport and Goresky-MacPherson

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dc.creatorSaper, Leslie
dc.date2001-12-22
dc.date2005-05-13
dc.date.accessioned2026-07-07T04:45:27Z
dc.date.available2026-07-07T04:45:27Z
dc.descriptionConsider 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.
dc.description16 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
dc.identifierhttps://arxiv.org/abs/math/0112250
dc.identifierhttp://arxiv.org/abs/math/0112250
dc.identifierFormes 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
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62959
dc.subjectRepresentation Theory
dc.subjectDifferential Geometry
dc.subject11F75, 22E40, 32S60, 55N33 (Primary) 14G35, 22E45 (Secondary)
dc.titleL-modules and the Conjecture of Rapoport and Goresky-MacPherson
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