Une caractérisation 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 $\overline{S}$.

arXiv comment4 pages. In french