The work of Mazur and Wiles on cyclotomic fields

John Coates

Displaying similar documents to “The work of Mazur and Wiles on cyclotomic fields”

$p$ -adic representations arising from descent on abelian varieties

Michael Harris (1979)

Compositio Mathematica

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Class groups of abelian fields, and the main conjecture

Cornelius Greither (1992)

Annales de l'institut Fourier

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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 $p = 2$ , 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 $χ$ -parts of $p$ -class groups of abelian number fields: first for relative class groups of real fields (again including the case $p = 2$ ). As a consequence, a generalization of the Gras conjecture...