L^2-cohomology of locally symmetric spaces, I

Details L^2-cohomology of locally symmetric spaces, I L^2-cohomology of locally symmetric spaces, I

2004-12-20

arxiv.org/abs/math/0412353v3

Pure Appl. Math. Q. 1 (2005), no. 4, 889-937

Mathematics

Representation Theory

40 pages, AMS-LaTeX, uses Xy-pic 3.7 package; v2: minor typos fixed, minor improvements in exposition, treatment in 10.4 of ho

Scientific paper

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 L^2-cohomology. In particular we construct an L-module whose cohomology is the L^2-cohomology of X and we calculate its micro-support. As an application we obtain a new proof of the conjectures of Borel and Zucker.

Affiliated with

Also associated with

No associations

Rating

L^2-cohomology of locally symmetric spaces, I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with L^2-cohomology of locally symmetric spaces, I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and L^2-cohomology of locally symmetric spaces, I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-121782