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arXiv · 2602.00615

On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication

Shun Ishii
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Abstract

We study a graded Lie algebra arising from the Galois action on the pro-$p$ 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.

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Shun Ishii. 2026-01-31. On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication. https://arxiv.org/abs/2602.00615

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