×

zbMATH — the first resource for mathematics

On polarised class groups of orders in quartic CM-fields. (English) Zbl 1417.11114
Summary: 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 endomorphism rings of abelian surfaces over finite fields, and we use our results to extend a completeness result of N. Murabayashi and A. Umegaki [J. Algebra 235, No. 1, 267–274 (2001; Zbl 0974.14015)] to a list of abelian surfaces over the rationals with complex multiplication by arbitrary orders.

MSC:
11G15 Complex multiplication and moduli of abelian varieties
14K15 Arithmetic ground fields for abelian varieties
11R65 Class groups and Picard groups of orders
PDF BibTeX XML Cite
Full Text: DOI arXiv