Diagrams in the mod <i>p</i> cohomology of Shimura curves
Diagrams in the mod <i>p</i> cohomology of Shimura curves
Abstract We prove a local–global compatibility result in the mod $p$ Langlands program for $\mathrm {GL}_2(\mathbf {Q}_{p^f})$ . Namely, given a global residual representation $\bar {r}$ appearing in the mod $p$ cohomology of a Shimura curve that is sufficiently generic at $p$ and satisfies a Taylor–Wiles hypothesis, we prove that …