Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The densest lattices in PGL3(Q2)   We find the smallest possible covolume for lattices in PGL3(Q2), show that
there are exactly two lattices with this covolume, and describe them
explicitly. They are commensurable, and one of them appeared in Mumford's
construction of his fake projective plane. We also discuss a new 2-adic
uniformization of another fake projective plane.

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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: q-fin