Class numbers of CM algebraic tori, CM abelian varieties and components of unitary Shimura varieties

2019/05/28 by Guo, Jia-Wei, Nai-Heng Sheu, Sheu, Nai-Heng +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1905.11649

openalex publication_date 2019/05/28 · openalex created_date 2019/06/07 · openalex updated_date 2026/07/28

Abstract

We give a formula for the class number of an arbitrary CM algebraic torus over ℚ. This is proved based on results of Ono and Shyr. As applications, we give formulas for numbers of polarized CM abelian varieties, of connected components of unitary Shimura varieties and of certain polarized abelian varieties over finite fields. We also give a second proof of our main result.

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