Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Base change of twisted Fontaine-Faltings modules and Twisted Higgs-de
  Rham flows over very ramified valuation rings   In this short notes, we prove a stronger version of Theorem 0.6 in our
previous paper arXiv:1709.01485: Given a smooth log scheme $(\mathcal{X}
\supset \mathcal{D})_{W(\mathbb{F}_q)}$, each stable twisted $f$-periodic
logarithmic Higgs bundle $(E,\theta)$ over the closed fiber $(X \supset
D)_{\mathbb{F}_q}$ will correspond to a
$\mathrm{PGL}_r(\mathbb{F}_{p^f})$-crystalline representation of
$\pi_1((\mathcal{X} \setminus \mathcal{D})_{W(\mathbb{F}_q)[\frac{1}{p}]})$
such that its restriction to the geometric fundamental group is absolutely
irreducible.

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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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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: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg