Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert-Mumford stability on algebraic stacks and applications to
  $\mathcal{G}$-bundles on curves   In these notes we reformulate the classical Hilbert-Mumford criterion for GIT
stability in terms of algebraic stacks, this was independently done by
Halpern-Leinster. We also give a geometric condition that guarantees the
existence of separated coarse moduli spaces for the substack of stable objects.
This is then applied to construct coarse moduli spaces for torsors under
parahoric group schemes over curves.

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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: gr-qc