On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication
Number Theory
2026-02-03 v1
Abstract
We study a graded Lie algebra arising from the Galois action on the pro- fundamental group of a once-punctured elliptic curve with complex multiplication. Among other things, we provide a minimal generating set of the rationalized Lie algebra under suitable assumptions. The proof is based on a slight variant of the theory of weighted completion of profinite groups developed by Hain and Matsumoto.
Cite
@article{arxiv.2602.00615,
title = {On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication},
author = {Shun Ishii},
journal= {arXiv preprint arXiv:2602.00615},
year = {2026}
}
Comments
19 pages, submitted