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Trivial Iwasawa modules and arithmetic linking numbers

  • Yasushi Mizusawa
  • Keiji Okano
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Abstract

We give a computable criterion of the triviality of the unramified Iwasawa module over the maximal multiple ℤp-extension of a number filed in which an odd prime number p splits completely. This criterion is obtained from the description of the presentation matrix of the Galois coinvariant of the Iwasawa module by arithmetic linking numbers. The description is based on the Koch type presentation of a pro-p Galois group with restricted ramification, which is analogous to the Milnor presentation of a link group from a viewpoint of arithmetic topology.

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Cite

BibTeXRIS
BibTeX
@misc{mizusawa2026trivial,
  title = {{Trivial Iwasawa modules and arithmetic linking numbers}},
  author = {Yasushi Mizusawa and Keiji Okano},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31965},
  eprint = {2610.31965},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31965},
}
RIS
TY  - UNPB
TI  - Trivial Iwasawa modules and arithmetic linking numbers
AU  - Yasushi Mizusawa
AU  - Keiji Okano
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31965
UR  - https://arxiv.org/abs/2610.31965
AB  - We give a computable criterion of the triviality of the unramified Iwasawa module over the maximal multiple ℤ_p-extension of a number filed in which an odd prime number p splits completely. This criterion is obtained from the description of the presentation matrix of the Galois coinvariant of the Iwasawa module by arithmetic linking numbers. The description is based on the Koch type presentation of a pro-p Galois group with restricted ramification, which is analogous to the Milnor presentation of a link group from a viewpoint of arithmetic topology.
ER  -