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.
Bibliographical noteFunding Information:
This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD), KRF-2006-331-C00003.
All Science Journal Classification (ASJC) codes
- Applied Mathematics