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 language | English |
|---|---|
| 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)
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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 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 -