Multivariable de Rham representations, Sen theory and $p$-adic differential equations

Olivier Brinon, Bruno Chiarellotto, Nicola Mazzari

Let $K$ be a complete valued field extension of ${\mathbf{Q}}_p$ with perfect residue field. We consider $p$-adic representations of a finite product $G_{K,\Delta }=G_K^{\Delta }$ of the absolute…