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

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 $\overline{S}$.