English

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-pp 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.

Keywords

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