Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of congruence subgroups of SL_3(Z), Steinberg modules, and
  real quadratic fields   We investigate the homology of a congruence subgroup Gamma of SL_3(Z) with
coefficients in the Steinberg modules St(Q^3) and St(E^3), where E is a real
quadratic field and the coefficients are Q. By Borel-Serre duality, H_0(Gamma,
St(Q^3)) is isomorphic to H^3(Gamma,Q). Taking the image of the connecting
homomorphism H_1(Gamma, St(E^3)/St(Q^3)) \to H_0(Gamma, St(Q^3)), followed by
the Borel-Serre isomorphism, we obtain a naturally defined Hecke-stable
subspace H(Gamma,E) of H^3(Gamma,Q). We conjecture that H(Gamma,E) is
independent of E and consists of the cuspidal cohomology H_cusp^3(Gamma,Q) plus
a certain subspace of H^3(Gamma, Q)$ that is isomorphic to the sum of the
cuspidal cohomologies of the maximal faces of the Borel-Serre boundary.
  We report on computer calculations of H(Gamma,E) for various Gamma, E which
provide evidence for the conjecture. We give a partial heuristic for the
conjecture.

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The categories of this paper are: stat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int