Article contents
The
$A_{\text{inf}}$-cohomology in the semistable case
Published online by Cambridge University Press: 09 September 2019
Abstract
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
$H_{\text{dR}}^{i}(X/K)$ 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
$A_{\text{inf}}$-valued cohomology theory of
$p$-adic formal, proper, smooth
${\mathcal{O}}_{\overline{K}}$-schemes
$\mathfrak{X}$ to the semistable case. The relation of the
$A_{\text{inf}}$-cohomology to the
$p$-adic étale and the logarithmic crystalline cohomologies allows us to reprove the semistable conjecture of Fontaine–Jannsen.
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- Research Article
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- Copyright
- © The Authors 2019
References
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