Compatibility of certain integral models of Shimura varieties of abelian type

TL;DR

This paper proves that certain integral models of Shimura varieties of abelian type are independent of auxiliary choices and discusses extending morphisms to these models, enhancing understanding of their structure.

Contribution

It demonstrates the independence of parahoric integral models from auxiliary data choices and provides partial results on extending morphisms.

Findings

Parahoric integral models are independent of auxiliary data choices.

Partial results on extending morphisms to integral models.

Improved understanding of the structure of Shimura varieties.

Abstract

For a prime $p>2$, Kisin and Pappas constructed parahoric integral models at $p$ for Shimura varieties attached to Shimura data $(G,X)$ of abelian type such that $G$ splits over a tamely ramified extension of $\mathbb{Q}_p$. A certain auxiliary data has to be chosen in their constructions. In this note, we will show that the parahoric integral models are actually independent of the choices of the auxiliary data. We also get partial results on extending morphisms of Shimura varieties to those of parahoric integral models.