On S-ramified T-split Iwasawa modules

TL;DR

This paper corrects previous formulas and computes defect groups for Iwasawa invariants in S-ramified T-split extensions, extending known results on tamely ramified Iwasawa modules for cyclotomic Z-l extensions of abelian fields.

Contribution

It provides corrected formulas and extends the understanding of Iwasawa modules in S-ramified T-split extensions, building on prior work by Itoh, Mizusawa, and Ozaki.

Findings

Corrected formulas for Iwasawa invariants.

Computed defect groups for specific extensions.

Extended results to broader class of abelian fields.

Abstract

We correct the faulty formulas given in a previous article and we compute the defect group for the Iwasawa $\lambda$ invariants attached to the S-ramified T-decomposed a belian pro-${\ell}$-extensions on the Z${\ell}$-cyclotomic extensionof a number field. As a consequence, we extend the results of Itoh, Mizusawa and Ozaki on tamely ramified Iwasawa modules for the cyclotomic Z${\ell}$-extension of abelian fields.