Conjectures and results on modular representations of ${\mathrm{GL}}_n(K)$ for a $p$-adic field $K$

Christophe Breuil, Florian Herzig, Yongquan Hu +2

Let $p$ be a prime number and $K$ a finite extension of ${\mathbb{Q}}_p$. We state conjectures on the smooth representations of ${\mathrm{GL}}_n(K)$ that occur in spaces of mod $p$ aut…