Current Developments in Mathematics
- Current Developments in Mathematics
- Volume 2002 (2002), 219-289.
On the Cohomology of Locally Symmetric Spaces and of their Compactifications
This expository article 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 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.
Current Developments in Mathematics Volume 2002 (2002), 219-289.
First available in Project Euclid: 29 June 2004
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Saper, Leslie. On the Cohomology of Locally Symmetric Spaces and of their Compactifications. Current Developments in Mathematics 2002 (2002), 219--289.https://projecteuclid.org/euclid.cdm/1088530402