Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher finiteness properties of reductive arithmetic groups in positive
  characteristic: the rank theorem   We show that the finiteness length of an $S$-arithmetic subgroup $\Gamma$ in
a noncommutative isotropic absolutely almost simple group $G$ over a global
function field is one less than the sum of the local ranks of $G$ taken over
the places in $S$. This determines the finiteness properties for arithmetic
subgroups in isotropic reductive groups, confirming the conjectured finiteness
properties for this class of groups. Our main tool is Behr-Harder reduction
theory which we recast in terms of the metric structure of euclidean buildings.

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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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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: dg-ga