Cornacchia, Pietro Fitting ideals of class groups in a \(\mathbb{Z}_p\)-extension. (English) Zbl 0926.11084 Acta Arith. 87, No. 1, 79-88 (1998). The author first proves a result about the module of Iwasawa algebra, which is finitely generated as \(\mathbb{Z}_p\)-module. The result can be roughly described as follows: the cohomology groups at finite levels determine the \(\mathbb{Z}_p\)-torsion part and the characteristic ideal gives information on the \(\mathbb{Z}_p\)-free part. As an application of this result, the author proves that the Fitting ideal of the \(\chi\)-parts of the ideal class group is equal to the fitting ideal of the \(\chi\)-parts of the group of units modulo cyclotomic units in any finite level for the cyclotomic \(\mathbb{Z}_p\)-extension of a totally real abelian number field and \(p\)-adic character \(\chi\) of this field. Reviewer: Xu Fei (Münster) Cited in 1 Document MSC: 11R29 Class numbers, class groups, discriminants 11R23 Iwasawa theory 11R18 Cyclotomic extensions Keywords:\(\mathbb{Z}_p\)-extension; Tate cohomology group; ideal class group; Iwasawa algebra; Fitting ideal PDF BibTeX XML Cite \textit{P. Cornacchia}, Acta Arith. 87, No. 1, 79--88 (1998; Zbl 0926.11084) Full Text: DOI EuDML