On Kummer characters arising from Galois actions on the pro-$p$ fundamental groups of once-punctured CM elliptic curves
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910003784318976 |
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| author | Ishii, Shun |
| author_facet | Ishii, Shun |
| contents | 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 Soulé characters. We investigate various arithmetic assumptions under which such characters are nontrivial or even surjective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04175 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Kummer characters arising from Galois actions on the pro-$p$ fundamental groups of once-punctured CM elliptic curves Ishii, Shun Number Theory 1G05, 11R23, 11R32, 12E30 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 Soulé characters. We investigate various arithmetic assumptions under which such characters are nontrivial or even surjective. |
| title | On Kummer characters arising from Galois actions on the pro-$p$ fundamental groups of once-punctured CM elliptic curves |
| topic | Number Theory 1G05, 11R23, 11R32, 12E30 |
| url | https://arxiv.org/abs/2312.04175 |