Math @ Duke

Publications [#305514] of Leslie Saper
Papers Published
 Saper, L, L²cohomology of locally symmetric spaces. I,
Pure and Applied Mathematics Quarterly, vol. 1 no. 4
(2005),
pp. 889937 [MR2201005], [arXiv:math/0412353], [0412353v3], [doi]
(last updated on 2018/10/16)
Abstract: Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. Lmodules are a combinatorial analogue of constructible sheaves on the reductive BorelSerre compactification of X; they were introduced in [math.RT/0112251]. That paper also introduced the microsupport of an Lmodule, 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 BorelSerre 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 L²cohomology. In particular we construct an Lmodule whose cohomology is the L²cohomology of X and we calculate its microsupport. As an application we obtain a new proof of the conjectures of Borel and Zucker.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

