On Shimura varieties for unitary groups
Number Theory
2020-08-27 v2 Algebraic Geometry
Representation Theory
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.
Cite
@article{arxiv.1906.12346,
title = {On Shimura varieties for unitary groups},
author = {Michael Rapoport and Brian Smithling and Wei Zhang},
journal= {arXiv preprint arXiv:1906.12346},
year = {2020}
}
Comments
39 pages. Minor modifications. This version is the final one, to appear in Pure and Applied Mathematics Quarterly (special issue in honor of D. Mumford)