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Truncated Euler Systems over Imaginary Quadratic Fields
Published online by Cambridge University Press: 11 January 2016
Abstract
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Let K be an imaginary quadratic field and let F be an abelian extension of K. It is known that the order of the class group ClF of F is equal to the order of the quotient UF /ElF of the group of global units UF by the group of elliptic units ElF of F. We introduce a filtration on UF /ElF 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 provide evidence for the conjecture using Iwasawa theory.
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