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arXiv · 1302.3756

On polarised class groups of orders in quartic CM-fields

Gaetan Bisson·Marco Streng
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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.

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Gaetan Bisson, Marco Streng. 2013-02-15. On polarised class groups of orders in quartic CM-fields. https://doi.org/10.4310/mrl.2017.v24.n2.a1

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