### Abstract

Let K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group Cl_{F} of F is equal to the order of the quotient U_{F}/El_{F} of the group of global units U_{F} by the group of elliptic units El_{F} of F. We introduce a filtration on U_{F} /El_{F} made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.

Original language | English |
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Pages (from-to) | 97-111 |

Number of pages | 15 |

Journal | Nagoya Mathematical Journal |

Volume | 195 |

Publication status | Published - 2009 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Nagoya Mathematical Journal*,

*195*, 97-111.

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*Nagoya Mathematical Journal*, vol. 195, pp. 97-111.

**Truncated euler systems over imaginary quadratic fields.** / Seo, Soogil.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Truncated euler systems over imaginary quadratic fields

AU - Seo, Soogil

PY - 2009/12/1

Y1 - 2009/12/1

N2 - Let K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF /ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.

AB - Let K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF/ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF /ElF made from the so-called truncated Euler systems and conjecture that the associated graded module is isomorphic, as a Galois module, to the class group. We provide evidence for the conjecture using Iwasawa theory.

UR - http://www.scopus.com/inward/record.url?scp=77949289192&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949289192&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77949289192

VL - 195

SP - 97

EP - 111

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -