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 |
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Pages (from-to) | 97-111 |
Number of pages | 15 |
Journal | Nagoya Mathematical Journal |
Volume | 195 |
DOIs | |
Publication status | Published - 2009 |
All Science Journal Classification (ASJC) codes
- Mathematics(all)