Construction of Galois modules describing ideal class groups and applications to Iwasawa theory

For a finite Galois extension of number fields, the ideal class groups of intermediate fields do not behave well under taking Galois coinvariants in general. In this paper, we construct a Galois module whose Galois coinvariants explicitly describe the ideal class groups of the intermediate fields. As an application, we demonstrate how this construction naturally yields some results in classical Iwasawa theory.