On polarised class groups of orders in quartic CM-fields
MATHEMATICAL RESEARCH LETTERS(2017)
摘要
We give an explicit necessary condition for pairs of orders in a quartic CM-field to have the same polarised class group. This generalises a simpler result for imaginary quadratic fields. We give an application of our results to computing endomor-phism rings of abelian surfaces over finite fields, and we use our results to extend a completeness result of Murabayashi and Umegaki [14] to a list of abelian surfaces over the rationals with complex multiplication by arbitrary orders.
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