Fargues-Rapoport conjecture in the non-basic case

Abstract: Rapoport and Zink introduce the p-adic period domain (also called the admissible locus) inside the rigid analytic p-adic flag varieties. Over the admissible locus, there exists a universal crystalline Qp-local system which interpolates a family of crystalline representations. The weakly admissible locus is an approximation of the admissible locus in the sense that these two spaces have the same classical points. In a joint work with Fargues and Shen, we prove the Fargues-Rapoport conjecture for basic local Shimura datum which gives a group theoretic characterization when the admissible locus and the weakly admissible locus coincide. In this talk, we will give a similiar criterion for non-basic local Shimura datum which generalizes the work of Hartl for GLn.

Mathematics

Audience: researchers in the topic

ICCM 2020