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Truncated Euler systems. (English) Zbl 1204.11170
Summary: 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 introduce a 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.

##### MSC:
 11R23 Iwasawa theory 11G16 Elliptic and modular units 11R27 Units and factorization 11R29 Class numbers, class groups, discriminants
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