Fonctions d'une variable $p$-adique et repr\'esentations de ${\rm GL}_2(\mathbf{Q}_p)$

Abstract

We extend the dictionary between Fontaine rings and $p$-adic functionnal analysis, and we give a refinement of the $p$-adic local Langlands correspondence for principal series representations of ${\rm GL}_2(\mathbf{Q}_p)$.