p-adic shtukas and the theory of global and local Shimura varieties

TL;DR

This paper develops foundational results on p-adic shtukas and applies them to construct integral models of local and global Shimura varieties of Hodge type, elucidating their interrelations.

Contribution

It introduces new foundational results on p-adic shtukas and constructs canonical integral models for Shimura varieties of Hodge type with parahoric level structure.

Findings

Established basic results on p-adic shtukas

Constructed canonical integral models for Shimura varieties

Clarified the relationship between local and global Shimura varieties

Abstract

We establish basic results on p-adic shtukas and apply them to the theory of local and global Shimura varieties, and on their interrelation. We construct canonical integral models for (local, and global) Shimura varieties of Hodge type with parahoric level structure.