Fitting ideals of $p$-ramified Iwasawa modules over totally real fields

TL;DR

This paper computes the Fitting ideal of p-ramified Iwasawa modules over totally real fields, extending previous results to more general ramification conditions using advanced derived category techniques.

Contribution

It provides a complete calculation of the Fitting ideal for classical p-ramified Iwasawa modules over abelian extensions of totally real fields, generalizing earlier work.

Findings

Explicit formulas for Fitting ideals in new ramification settings

Extension of previous results to broader classes of extensions

Use of derived categories for complex computations

Abstract

We completely calculate the Fitting ideal of the classical $p$-ramified Iwasawa module for any abelian extension $K/k$ of totally real fields, using the shifted Fitting ideals recently developed by the second author. This generalizes former results by the first and third authors where we had to assume that only $p$-adic places may ramify in $K/k$. One of the important ingredients is the computation of some complexes in appropriate derived categories.