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<p>In this paper, we study certain characters arising from the Galois actions on the pro-<i>p</i> geometric fundamental groups of once-punctured CM elliptic curves. These characters may be regarded as analogues of the Soulé characters, which arise from the Galois action associated to the thrice-punctured projective line. We study various arithmetic assumptions under which such characters are nontrivial or even surjective.</p>

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

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • Shun Ishii

摘要

In this paper, we study certain characters arising from the Galois actions on the pro-p geometric fundamental groups of once-punctured CM elliptic curves. These characters may be regarded as analogues of the Soulé characters, which arise from the Galois action associated to the thrice-punctured projective line. We study various arithmetic assumptions under which such characters are nontrivial or even surjective.