Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On absolutely profinitely solitary lattices in higher rank Lie groups   We establish conditions under which lattices in certain simple Lie groups are
profinitely solitary in the absolute sense, so that the commensurability class
of the profinite completion determines the commensurability class of the group
among finitely generated residually finite groups. While cocompact lattices are
typically not absolutely solitary, we show that noncocompact lattices in
$\operatorname{Sp}(n,\mathbb{R})$, $G_{2(2)}$, $E_8(\mathbb{C})$,
$F_4(\mathbb{C})$, and $G_2(\mathbb{C})$ are absolutely solitary if a
well-known conjecture on Grothendieck rigidity is true.

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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: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph