Isogeny graphs with level structures arrising from the Verschiebung map
Number Theory
2025-01-08 v1 Combinatorics
Abstract
We enhance an isogeny graph of elliptic curves by incorporating level structures defined by bases of the kernels of iterates of the Verschiebung map. We extend several previous results on isogeny graphs with level structures defined by geometric points to these graphs. Firstly, we prove that these graphs form -towers of graph coverings as the power of the Verschiebung map varies. Secondly, we prove that the connected components of these graphs display a volcanic structure.
Cite
@article{arxiv.2501.03846,
title = {Isogeny graphs with level structures arrising from the Verschiebung map},
author = {Antonio Lei and Katharina Müller},
journal= {arXiv preprint arXiv:2501.03846},
year = {2025}
}
Comments
To appear in the proceedings of the ICTS program "Elliptic curves and the special values of L-functions"