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arXiv · 2509.12425

Une caractérisation de $\mathbb{B}_{\mathrm{dR}}^+$ et $\mathcal{O}\mathbb{B}_{\mathrm{dR}}^+$

Pierre Colmez
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Abstract

We show that ${\mathbf B}_{\mathrm{dR}}^+$ is the universal thickening of ${\mathbf C}_p$. More generally, we show that, if $S$ is a reduced affinoid algebra, $\mathcal{O}\mathbb{B}_{\mathrm{dR}}^+(\overline{S})$ is the universal $S$-thickening of the completion of $\overline{S}$.

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Pierre Colmez. 2025-09-15. Une caractérisation de $\mathbb{B}_{\mathrm{dR}}^+$ et $\mathcal{O}\mathbb{B}_{\mathrm{dR}}^+$. https://arxiv.org/abs/2509.12425

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