3 problems

Fargues–Scholze–Zhu global compatibility conjecture. Under this identification, the $\bigotimes_u\End_{G(F_u)}(\cInd_{G(\cO_u)}^{G(F_u)}\La)$-module $\loc_{Z,!}\!\La$ corresponds t…

Kottwitz's multiplicity conjecture. The multiplicity of $\pi$ in the discrete spectrum of $G$ is given by

Global L-packet and discrete-spectrum conjecture. One can associate a global packet $\bar\Pi_{\widetilde\phi}$ of $\bar{\mathcal H}(\widetilde G)$-modules of irreducible admissible…