On Kummer characters arising from Galois actions on the pro-$p$ fundamental groups of once-punctured CM elliptic curves

Shun Ishii

doi:10.1007/s40993-025-00622-0

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arXiv · 2312.04175

On Kummer characters arising from Galois actions on the pro-$p$ fundamental groups of once-punctured CM elliptic curves

Shun Ishii

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Abstract

In this paper, we study certain Kummer characters arising from the pro-$p$ geometric fundamental groups of CM elliptic curves minus their origins (once-punctured CM elliptic curves). These characters may be regarded as analogues of the Soul\'e characters. We investigate various arithmetic assumptions under which such characters are nontrivial or even surjective.

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Shun Ishii. 2023-12-07. On Kummer characters arising from Galois actions on the pro-$p$ fundamental groups of once-punctured CM elliptic curves. https://doi.org/10.1007/s40993-025-00622-0

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