The canonicity of the integral models of RSZ Shimura varieties

TL;DR

This paper proves that certain integral models of RSZ Shimura varieties are canonical and isomorphic to models constructed by Kisin and Pappas, confirming their unique and well-defined nature in arithmetic geometry.

Contribution

It establishes the canonicity and uniqueness of integral models of RSZ Shimura varieties, linking them to Kisin and Pappas's constructions.

Findings

Integral models are canonical in Pappas's sense.

Models are isomorphic to Kisin and Pappas's models.

Supports conjectures in arithmetic Gan-Gross-Prasad and related areas.

Abstract

We show that the integral models of Shimura varieties of Rapoport, Smithling and Zhang in relation to variants of the arithmetic Gan-Gross-Prasad conjecture, the arithmetic fundamental lemma conjecture and the arithmetic transfer conjecture are canonical in the sense prescribed by Pappas. In particular, we prove that they are isomorphic to the models constructed by Kisin and Pappas.