TY - JOUR
T1 - Truncated euler systems over imaginary quadratic fields
AU - Seo, Soogil
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2009
Y1 - 2009
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.
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U2 - 10.1017/s0027763000009727
DO - 10.1017/s0027763000009727
M3 - Article
AN - SCOPUS:77949289192
VL - 195
SP - 97
EP - 111
JO - Nagoya Mathematical Journal
JF - Nagoya Mathematical Journal
SN - 0027-7630
ER -