5 problems

Fargues–Rapoport's conjecture. There exists a group-theoretic condition which expresses precisely when

Chai's density conjecture. If $K_p$ is hyperspecial, then the orbit of any point of ${\cal S}_{[b_\mu]}$ under $\bold G(\mathbb A_f^p)$ is dense in $\overline{Sh(G,h)}_{\bold K}$.

Chai's Newton-strata codimension conjecture. Every Newton stratum ${\cal S}_{[b]}$ is equidimensional, with codimension

Grothendieck's conjecture. The closure of the Newton stratum corresponding to $\nu$ is the union of the Newton strata corresponding to the Newton polygons lying below $\nu$.

Let $G_{{\mathbb Q}}\hookrightarrow \mathrm{GSp}_{{\mathbb Q}}$ and let $(G_{{\mathbb Q}},X)$ be a Shimura curve of Hodge type. Let…