On polarised class groups of orders in quartic CM-fields
Number Theory
2019-02-04 v6
Abstract
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.
Cite
@article{arxiv.1302.3756,
title = {On polarised class groups of orders in quartic CM-fields},
author = {Gaetan Bisson and Marco Streng},
journal= {arXiv preprint arXiv:1302.3756},
year = {2019}
}
Comments
19 pages, v2 strengthened results slightly and changed theorem numbering, v3 further strengthened results and added more details, v4 eased the presentation but changed notations and numbering, v5 updated references, v6 removes mistaken "transitivity" statement