Truncated euler systems over imaginary quadratic fields

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Pages (from-to)97-111
Number of pages15
JournalNagoya Mathematical Journal
Volume195
Publication statusPublished - 2009 Dec 1

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Euler System
Imaginary Quadratic Field
Class Group
Iwasawa Theory
Graded Module
Unit
Galois
Filtration
Quotient
Isomorphic
Module
Evidence

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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

In: Nagoya Mathematical Journal, Vol. 195, 01.12.2009, p. 97-111.

Research output: Contribution to journalArticle

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