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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.

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