On Shimura varieties for unitary groups

TL;DR

This paper explores the structure and properties of certain unitary Shimura varieties, focusing on their algebraic cycles and generalizing previous results to broader signature types.

Contribution

It introduces a new class of Shimura varieties related to unitary groups and extends prior work to arbitrary signature types, enhancing understanding of their algebraic cycles.

Findings

Defined a new class of Shimura varieties for unitary groups

Generalized previous results to arbitrary signature types

Compared these varieties with other unitary Shimura varieties

Abstract

This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian varieties with additional structure, and which admit interesting algebraic cycles. We generalize to arbitrary signature type the results of our previous work valid under special signature conditions. We compare our Shimura varieties with other unitary Shimura varieties.