Math @ Duke

Publications [#320537] of Leslie Saper
Papers Published
 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, ST
(2003),
pp. 219289, 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 2020/03/30)
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 GoreskyMacPherson which identifies
the intersection cohomology of a real equalrank Satake compactification of a
locally symmetric space with that of the reductive BorelSerre
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 Lmodules
and microsupport (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 Lmodules that lead to the resolution
of the conjecture. The text is enriched with many examples, illustrations, and
references to the literature.


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