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

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

2001-12-22

arxiv.org/abs/math/0112250v4

Formes Automorphes (I) -- Actes du Semestre du Centre \'Emile Borel, printemps 2000 (J. Tilouine, H. Carayol, M. Harris, and M

Mathematics

Representation Theory

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) co

Scientific paper

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.

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