Truncated Euler systems

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Abstract

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.

Original languageEnglish
Pages (from-to)53-71
Number of pages19
JournalJournal fur die Reine und Angewandte Mathematik
Issue number614
DOIs
Publication statusPublished - 2008 Dec 19

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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