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On finiteness properties of the unramified Iwasawa module of a ℤp-extension with restricted ramification
Abstract
In the present article, we consider ℤp-extensions defined by restrictions on ramification at p-adic primes. We study the finiteness, the existence of non-trivial finite submodules, and the triviality of the unramified Iwasawa modules of these ℤp-extensions. In addition, we give a new sufficient condition for Greenberg's Generalized Conjecture with some non-trivial concrete examples.
Related
- Abelian p-extensions with restricted p-ramification and the cyclotomic ℤ2-extension of ℚ (√q)
- Ramification and Finiteness of Equivariant Minimal Surfaces
- Multiplicator freeness for restricted-ramification Galois groups over global function fields
- Homological finiteness properties of wreath products
- Finiteness properties of profinite blocks and blocks with defect group ℤpn
BibTeX
@misc{yanagisawa2026finiteness,
title = {{On finiteness properties of the unramified Iwasawa module of a $\mathbbZ_p$-extension with restricted ramification}},
author = {Takuya Yanagisawa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.22324},
eprint = {2606.22324},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.22324},
}
RIS
TY - UNPB
TI - On finiteness properties of the unramified Iwasawa module of a ℤ_p-extension with restricted ramification
AU - Takuya Yanagisawa
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2606.22324
UR - https://arxiv.org/abs/2606.22324
AB - In the present article, we consider ℤ_p-extensions defined by restrictions on ramification at p-adic primes. We study the finiteness, the existence of non-trivial finite submodules, and the triviality of the unramified Iwasawa modules of these ℤ_p-extensions. In addition, we give a new sufficient condition for Greenberg's Generalized Conjecture with some non-trivial concrete examples.
ER -