On finiteness properties of the unramified Iwasawa module of a $\mathbb{Z}_p$-extension with restricted ramification
Year: 2026
Type: preprint
Abstract: In the present article, we consider $\mathbb{Z}_p$-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 $\mathbb{Z}_p$-extensions. In addition, we give a new sufficient condition for Greenberg's Generalized Conjecture with some non-trivial concrete examples.
Source: arXiv (Cornell University)
Author: Yanagisawa, Takuya
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7165666099