Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $A_{inf}$-cohomology in the semistable case   For a proper, smooth scheme $X$ over a $p$-adic field $K$, we show that any
proper, flat, semistable $\mathcal{O}_K$-model $\mathcal{X}$ of $X$ whose
logarithmic de Rham cohomology is torsion free determines the same
$\mathcal{O}_K$-lattice inside $H^i_{dR}(X/K)$ and, moreover, that this lattice
is functorial in $X$. For this, we extend the results of Bhatt--Morrow--Scholze
on the construction and the analysis of an $A_{inf}$-valued cohomology theory
of $p$-adic formal, proper, smooth $\mathcal{O}_{\overline{K}}$-schemes
$\mathfrak{X}$ to the semistable case. The relation of the $A_{inf}$-cohomology
to the $p$-adic \'{e}tale and the logarithmic crystalline cohomologies allows
us to reprove the semistable conjecture of Fontaine--Jannsen.

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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph