On polarised class groups of orders in quartic {CM}-fields

Author(s):
Bisson, G.; Streng, T.C. (0000-0001-9954-948X)
Published
2017
Publication type
Article / Letter to editor

Abstract

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.

Date issued
2017
Language
English
Is part of
Mathematical Research Letters (2017), Vol. 24, no. 2, p. 247-270
hdl
1887/57657
doi
10.4310/MRL.2017.v24.n2.a1
URL
https://arxiv.org/abs/1302.3756