Igusa stacks for certain abelian-type Shimura varieties

TL;DR

This paper constructs Igusa stacks for specific abelian-type Shimura varieties with good reduction, focusing on cases defined by PEL data of type (A even) or (C) that are unramified at prime p, advancing understanding of their geometric structures.

Contribution

It introduces a new construction of Igusa stacks for certain abelian-type Shimura varieties with specified PEL data and reduction properties.

Findings

Construction of Igusa stacks for specified Shimura varieties

Applicable to varieties of type (A even) or (C)

Assumes unramified conditions at prime p

Abstract

We construct Igusa stacks for the good reduction locus of a class of abelian-type Shimura varieties that can be defined in terms of a PEL datum, under the assumption that it is of type (A even) or (C) and unramified at a prime p.