Integral models in unramified mixed characteristic (0,2) of hermitian orthogonal Shimura varieties of PEL type, Part I

TL;DR

This paper establishes the existence of integral canonical models for certain PEL-type Shimura varieties in unramified mixed characteristic (0,2), focusing on cases where the group is split GSO_{2n} over Q_2.

Contribution

It proves the existence of integral canonical models for unramified mixed characteristic (0,2) Shimura varieties of PEL type with split GSO_{2n} groups over Q_2.

Findings

Existence of integral canonical models in unramified mixed characteristic (0,2)

Construction for Shimura varieties with split GSO_{2n} groups

Validation of models over hyperspecial subgroups

Abstract

Let $(G,X)$ be a Shimura variety of PEL type such that $G_{{\bf Q}_2}$ is a split ${\bf GSO}_{2n}$ group with $n\ge 2$. We prove the existence of the integral canonical models of ${\rm Sh}(G,X)/H_2$ in unramified mixed characteristic $(0,2)$, where $H_2$ is a hyperspecial subgroup of $G({\bf Q}_2)$.