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- On polarised class groups of orders in quartic {CM}-fields
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On polarised class groups of orders in quartic {CM}-fields
https://arxiv.org/abs/1302.3756
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.
- All authors
- Bisson, G.; Streng, T.C.
- Date
- 2017
- Journal
- Mathematical Research Letters
- Volume
- 24
- Issue
- 2
- Pages
- 247 - 270