Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge type theorems for arithmetic manifolds associated to orthogonal
  groups   We show that special cycles generate a large part of the cohomology of
locally symmetric spaces associated to orthogonal groups. We prove in
particular that classes of totally geodesic submanifolds generate the
cohomology groups of degree $n$ of compact congruence $p$-dimensional
hyperbolic manifolds "of simple type" as long as $n$ is strictly smaller than
$\frac{p}{3}$. We also prove that for connected Shimura varieties associated to
$\OO (p,2)$ the Hodge conjecture is true for classes of degree $<
\frac{p+1}{3}$. The proof of our general theorem makes use of the recent
endoscopic classification of automorphic representations of orthogonal groups
by \cite{ArthurBook}. As such our results are conditional on the hypothesis
made in this book, whose proofs have only appear on preprint form so far; see
the second paragraph of subsection \ref{org2} below.

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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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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: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th