Class groups of abelian fields, and the main conjecture
The 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 \(\chi\)-parts of p-class groups of abelian number fields: first for relative class groups as has been done recently by Solomon for odd p, and second for class groups of real fields (again including the case \(p=2)\). As a consequence, a generalization of the Gras conjecture is stated and proved.
scientific article; zbMATH DE number 4204471
scientific article