Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L^2-cohomology of locally symmetric spaces, I   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.

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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: hep-ex