L^2-cohomology of locally symmetric spaces, I
Abstrak
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.
Topik & Kata Kunci
Penulis (1)
Leslie Saper
Akses Cepat
- Tahun Terbit
- 2004
- Bahasa
- en
- Total Sitasi
- 9×
- Sumber Database
- Semantic Scholar
- DOI
- 10.4310/PAMQ.2005.V1.N4.A9
- Akses
- Open Access ✓