### Abstract

It is known that the order of the class group Cl _{K} of the real abelian field K is essentially equal to the order of the quotient E _{K}/C _{K} of the global units E _{K} by the circular units C _{K} of K. However, the structures of these two groups are usually very different. Motivated by the theory of circular distributions and the special units of Rubin, we introducea filtration to E _{K} 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 use Euler systems to give evidence for this conjecture.

Original language | English |
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Pages (from-to) | 53-71 |

Number of pages | 19 |

Journal | Journal fur die Reine und Angewandte Mathematik |

Issue number | 614 |

DOIs | |

Publication status | Published - 2008 Dec 19 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Journal fur die Reine und Angewandte Mathematik*, no. 614, pp. 53-71. https://doi.org/10.1515/CRELLE.2008.002

**Truncated Euler systems.** / Seo, Soogil.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Truncated Euler systems

AU - Seo, Soogil

PY - 2008/12/19

Y1 - 2008/12/19

N2 - It is known that the order of the class group Cl K of the real abelian field K is essentially equal to the order of the quotient E K/C K of the global units E K by the circular units C K of K. However, the structures of these two groups are usually very different. Motivated by the theory of circular distributions and the special units of Rubin, we introducea filtration to E K 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 use Euler systems to give evidence for this conjecture.

AB - It is known that the order of the class group Cl K of the real abelian field K is essentially equal to the order of the quotient E K/C K of the global units E K by the circular units C K of K. However, the structures of these two groups are usually very different. Motivated by the theory of circular distributions and the special units of Rubin, we introducea filtration to E K 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 use Euler systems to give evidence for this conjecture.

UR - http://www.scopus.com/inward/record.url?scp=77949305906&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77949305906&partnerID=8YFLogxK

U2 - 10.1515/CRELLE.2008.002

DO - 10.1515/CRELLE.2008.002

M3 - Article

SP - 53

EP - 71

JO - Journal fur die Reine und Angewandte Mathematik

JF - Journal fur die Reine und Angewandte Mathematik

SN - 0075-4102

IS - 614

ER -