On the equivariant Tamagawa number conjecture for Abelian extensions of a quadratic imaginary field.
Bley, W. (2006)
Documenta Mathematica
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Bley, W. (2006)
Documenta Mathematica
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This first part of this paper gives a proof of the main conjecture of Iwasawa theory for abelian base fields, including the case , by Kolyvagin’s method of Euler systems. On the way, one obtains a general result on local units modulo circular units. This is then used to deduce theorems on the order of -parts of -class groups of abelian number fields: first for relative class groups of real fields (again including the case ). As a consequence, a generalization of the Gras conjecture...
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