Publications [#320537] of Leslie Saper

Papers Published

1. Saper, L, On the Cohomology of Locally Symmetric Spaces and of their Compactifications, in Current developments in mathematics, 2002, edited by Jerison, D; Lusztig, G; Mazur, B; Mrowka, T; Schmid, W; Stanley, R; Yau, S-T (2003), pp. 219-289, International Press (reprinted in Lie Groups and Automorphic Forms, edited by L. Ji, et al., AMS/IP Studies in Advanced Mathematics, vol. 37, 2006.) [MR2062320], [arXiv:math/0306403]
   (last updated on 2024/04/19)

   Abstract:
   This expository article is an expanded version of talks given at the "Current Developments in Mathematics, 2002" conference. It gives an introduction to the (generalized) conjecture of Rapoport and Goresky-MacPherson which identifies the intersection cohomology of a real equal-rank Satake compactification of a locally symmetric space with that of the reductive Borel-Serre compactification. We motivate the conjecture with examples and then give an introduction to the various topics that are involved: intersection cohomology, the derived category, and compactifications of a locally symmetric space, particularly those above. We then give an overview of the theory of L-modules and micro-support (see math.RT/0112251) which was developed to solve the conjecture but has other important applications as well. We end with sketches of the proofs of three main theorems on L-modules that lead to the resolution of the conjecture. The text is enriched with many examples, illustrations, and references to the literature.