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

Jia-Wei Guo, Nai-Heng Sheu, Chia-Fu Yu

We give a formula for the class number of an arbitrary CM algebraic torus over $\mathbb{Q}$. This is proved based on results of Ono and Shyr. As applications, we give formulas for…