Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perversity equals weight for Painlev\'e spaces   We provide further evidence to the $P=W$ conjecture of de Cataldo, Hausel and
Migliorini, by checking it in the Painlev\'e cases. Namely, we compare the
perverse Leray filtration induced by the Hitchin map on the cohomology spaces
of the Dolbeault moduli space and the weight filtration on the cohomology
spaces of the irregular character variety corresponding to each of the
Painlev\'e $I-VI$ systems. We find that the two filtrations agree. Along the
way, we prove the Geometric $P=W$ conjecture of Katzarkov, Noll, Pandit and
Simpson in the Painlev\'e cases, and show that in these cases the Geometric
$P=W$ conjecture implies the $P=W$ conjecture.

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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom