On a generalization of Tate dualities with application to Iwasawa theory

Li Guo

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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...

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A new proof is given of the connecting homomorphism.