On Shimura varieties for unitary groups

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.

arXiv comment39 pages. Minor modifications. This version is the final one, to appear in Pure and Applied Mathematics Quarterly (special issue in honor of D. Mumford)

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Cited by in corpus (3)

• Kudla--Rapoport cycles and derivatives of local densities
• Weil representation and Arithmetic Fundamental Lemma
• On the Arithmetic Fundamental Lemma conjecture over a general $p$-adic field