# Diagrams in the mod $p$ cohomology of Shimura curves

26 Sep 2019 Dotto Andrea Le Daniel

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 $\bar{r}$ that is sufficiently generic at $p$, we prove that the diagram occurring in the corresponding Hecke eigenspace of completed cohomology is determined by the restrictions of $\bar{r}$ to decomposition groups at $p$... (read more)

PDF Abstract

# Code Add Remove Mark official

No code implementations yet. Submit your code now

# Categories

• NUMBER THEORY
• REPRESENTATION THEORY