Publications [#305514] of Leslie Saper

Papers Published

1. Saper, L, L²-cohomology of locally symmetric spaces. I, Pure and Applied Mathematics Quarterly, vol. 1 no. 4 (2005), pp. 889-937, International Press of Boston [MR2201005], [arXiv:math/0412353], [0412353v3], [doi]
   (last updated on 2024/04/22)

   Abstract:
   Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of X; they were introduced in [math.RT/0112251]. That paper also introduced the micro-support of an L-module, a combinatorial invariant that to a great extent characterizes the cohomology of the associated sheaf. The theory has been successfully applied to solve a number of problems concerning the intersection cohomology and weighted cohomology of the reductive Borel-Serre compactification [math.RT/0112251], as well as the ordinary cohomology of X [math.RT/0112250]. In this paper we extend the theory so that it covers L²-cohomology. In particular we construct an L-module whose cohomology is the L²-cohomology of X and we calculate its micro-support. As an application we obtain a new proof of the conjectures of Borel and Zucker.