On the Hodge embedding for PEL type integral models of Shimura varieties

TL;DR

This paper proves that PEL type integral models of Shimura varieties can be embedded into Siegel models and shows their agreement with other established models, clarifying their structure and relationships.

Contribution

It provides a simple proof of embeddings of PEL integral models into Siegel models and confirms their equivalence with Kisin's models for relevant data.

Findings

PEL integral models admit closed embeddings into Siegel models

Rapoport's and Kottwitz's models agree with Kisin's models

Clarifies the structure and relationships of Shimura variety models

Abstract

We give a simple proof that Kottwitz's PEL type integral models of Shimura varieties admit closed embeddings into Siegel integral models. We also show that Rapoport's and Kottwitz's integral models agree with Kisin's integral models for relevant Shimura data.