Frobenius lifts and elliptic curves with complex multiplication
Number Theory
2021-11-10 v3
Abstract
We give a new characterisation of elliptic curves of Shimura type in terms commuting families of Frobenius lifts and also strengthen an old principal ideal theorem for ray class fields. These two results combined yield the existence of global minimal models for elliptic curves of Shimura type, generalising a result of Gross. Along the way we also prove a handful of small but new results regarding elliptic curves with complex multiplication.
Cite
@article{arxiv.1910.14358,
title = {Frobenius lifts and elliptic curves with complex multiplication},
author = {Lance Gurney},
journal= {arXiv preprint arXiv:1910.14358},
year = {2021}
}