On graded Lie algebras associated to once-punctured elliptic curves with complex multiplication
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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Algebraic Geometry and Number Theory
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 31 January 2026
- Document type
- Preprint