Langlands–Rapoport conjecture for mod p points of integral canonical models

Prove the Langlands–Rapoport conjecture by establishing the precise description of the mod p points of the integral canonical models of Shimura varieties Sh_K(G,X) over the ring of integers of their reflex field E(G,X), including in the non-abelian type cases.

Background

The paper discusses the motivic expectations for Shimura varieties and the existence of integral canonical models over the ring of integers of the reflex field. While compatibility of coefficient objects is the focus of the current work, the authors explicitly reference the Langlands–Rapoport conjecture concerning a detailed description of mod p points of these integral models as a major surrounding conjecture.

This conjecture is central in the broader program connecting Shimura varieties, Galois representations, and arithmetic geometry, and remains open in general, particularly outside abelian type settings.