Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $p$-adic Corlette-Simpson correspondence for abeloids   For an abeloid variety $A$ over a complete algebraically closed field
extension $K$ of $\mathbb Q_p$, we construct a $p$-adic Corlette-Simpson
correspondence, namely an equivalence between finite-dimensional continuous
$K$-linear representations of the Tate module and a certain subcategory of the
Higgs bundles on $A$. To do so, our central object of study is the category of
vector bundles for the $v$-topology on the diamond associated to $A$. We prove
that any pro-finite-\'etale $v$-vector bundle can be built from
pro-finite-\'etale $v$-line bundles and unipotent $v$-bundles. To describe the
latter, we extend the theory of universal vector extensions to the $v$-topology
and use this to generalise a result of Brion by relating unipotent $v$-bundles
on abeloids to representations of vector groups.

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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: cs
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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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: cmp-lg
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The categories of this paper are: hep-ex