Multivariable ($\phi$,${\mathcal{O}}_K^{\times }$)-modules and local-global compatibility

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number, $K$ a finite unramified extension of ${\mathbb{Q}}_p$ and $\mathbb{F}$ a finite extension of ${\mathbb{F}}_p$. Using perfectoid spaces we associate to any fi…