Mathematical Research Letters
Volume 24 (2017)
On polarised class groups of orders in quartic CM-fields
Pages: 247 – 270
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 Murabayashi and Umegaki to a list of abelian surfaces over the rationals with complex multiplication by arbitrary orders.
Received 1 October 2013
Accepted 7 November 2015
Published 24 July 2017