Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Complete integrability of the parahoric Hitchin system   Let $\mathcal{G}$ be a parahoric group scheme over a complex projective curve
$X$ of genus greater than one. Let $\mathrm{Bun}_{\mathcal{G}}$ denote the
moduli stack of $\mathcal{G}$-torsors on $X$. We prove several results
concerning the Hitchin map on $T^*\!\mathrm{Bun}_{\mathcal{G}}$. We first show
that the parahoric analogue of the global nilpotent cone is isotropic and use
this to prove that $\mathrm{Bun}_{\mathcal{G}}$ is "very good" in the sense of
Beilinson-Drinfeld. We then prove that the parahoric Hitchin map is a Poisson
map whose generic fibres are abelian varieties. Together, these results imply
that the parahoric Hitchin map is a completely integrable system.

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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: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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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: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: eess