On mod $p$ local-global compatibility for ${\mathrm{GL}}_n({\mathbf{Q}}_p)$ in the ordinary case

Chol Park, Zicheng Qian

Let $p$ be a prime number, $n>2$ an integer, and $F$ a CM field in which $p$ splits completely. Assume that a continuous automorphic Galois representation $\overline{r}:\mathrm{Gal…