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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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