### Abstract

Let E be an elliptic curve defined over Q with complex multiplication by the ring of integers of an imaginary quadratic field K. We apply an elliptic unit version of Ichimura-Sumida criterion for the Z_{p}-extension F∞/F associated to E and try to determine the characteristic polynomial of the maximal unramified abelian p-extension of F∞.

Original language | English |
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Pages (from-to) | 541-550 |

Number of pages | 10 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Volume | 137 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2004 Nov |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

_{p}-extensions associated to elliptic curves with complex multiplication.

*Mathematical Proceedings of the Cambridge Philosophical Society*,

*137*(3), 541-550. https://doi.org/10.1017/S0305004104007959

**ℤ _{p}-extensions associated to elliptic curves with complex multiplication.** / Fukuda, Takashi; Komatsu, Keiichi.

Research output: Contribution to journal › Article

_{p}-extensions associated to elliptic curves with complex multiplication',

*Mathematical Proceedings of the Cambridge Philosophical Society*, vol. 137, no. 3, pp. 541-550. https://doi.org/10.1017/S0305004104007959

_{p}-extensions associated to elliptic curves with complex multiplication. Mathematical Proceedings of the Cambridge Philosophical Society. 2004 Nov;137(3):541-550. https://doi.org/10.1017/S0305004104007959

}

TY - JOUR

T1 - ℤp-extensions associated to elliptic curves with complex multiplication

AU - Fukuda, Takashi

AU - Komatsu, Keiichi

PY - 2004/11

Y1 - 2004/11

N2 - Let E be an elliptic curve defined over Q with complex multiplication by the ring of integers of an imaginary quadratic field K. We apply an elliptic unit version of Ichimura-Sumida criterion for the Zp-extension F∞/F associated to E and try to determine the characteristic polynomial of the maximal unramified abelian p-extension of F∞.

AB - Let E be an elliptic curve defined over Q with complex multiplication by the ring of integers of an imaginary quadratic field K. We apply an elliptic unit version of Ichimura-Sumida criterion for the Zp-extension F∞/F associated to E and try to determine the characteristic polynomial of the maximal unramified abelian p-extension of F∞.

UR - http://www.scopus.com/inward/record.url?scp=10044274134&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10044274134&partnerID=8YFLogxK

U2 - 10.1017/S0305004104007959

DO - 10.1017/S0305004104007959

M3 - Article

AN - SCOPUS:10044274134

VL - 137

SP - 541

EP - 550

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 3

ER -