Fargues–Rapoport conjecture for $p$-adic period domains in the non-basic case

Abstract

We prove the Fargues–Rapoport conjecture for $p$-adic period domains in the non-basic case with minuscule cocharacter. More precisely, we give a group-theoretical criterion for the cases when the admissible locus and weakly admissible locus coincide. This generalizes the result of Hartl (2013) for the group ${\mathrm{GL}}_n$. In the last section, we also give a conjecture about the intersection of weakly admissible locus and the Newton strata in the flag variety.