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

  • Takenori Kataoka
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{kataoka2026construction,
  title = {{Construction of Galois modules describing ideal class groups and applications to Iwasawa theory}},
  author = {Takenori Kataoka},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29071},
  eprint = {2610.29071},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29071},
}
RIS
TY  - UNPB
TI  - Construction of Galois modules describing ideal class groups and applications to Iwasawa theory
AU  - Takenori Kataoka
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29071
UR  - https://arxiv.org/abs/2610.29071
AB  - 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.
ER  -