Class number behavior in a two-tiered tower of ℤ_p-extensions

2024/07/29 by Itoh, Tsuyoshi
#11R23 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2407.19751

Abstract

Let k_∞ be the cyclotomic ℤ_p-extension field of an algebraic number field k. Moreover, we take a ℤ_p-extension K_∞ over k_∞. In this paper, we study the behavior of the p-part of the class number of certain intermediate fields of K_∞ /k. We also consider the structure of the unramified Iwasawa module of K_∞ / k_∞ for several cases.

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