On Shimura varieties for unitary groups

2019/06/28 by Michael Rapoport, Rapoport, Michael, Brian D. Smithling +3 · 2 citations
Mathematics · #11G18 #14G35 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1906.12346

openalex publication_date 2019/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

Cited by

• Positive density of primes of ordinary reduction for abelian varieties of simple signature
• On the Arithmetic Fundamental Lemma conjecture over a general p-adic field

Related

• Arithmetic diagonal cycles on unitary Shimura varieties
• Special cycles on unitary Shimura varieties II: global theory
• Derived special cycles on Shimura varieties
• Congruence relations for Shimura varieties associated to some unitary groups
• Hecke and Galois Properties of Special Cycles on Unitary Shimura Varieties