On a bound of p-ranks of Iwasawa modules of ℤ_p-extensions over a quartic CM-field

2025/12/09 by Takuya Yanagisawa, Yanagisawa, Takuya
Mathematics · #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2512.08278

Abstract

Let p be a prime number. If a number field k has at least one complex place, there are infinitely many ℤ_p-extensions over k, and some authors studied the behavior of Iwasawa invariants of these ℤ_p-extensions. In particular, Fujii studied the case where k is an imaginary quadratic field and obtained some results on the boundedness of Iwasawa λ-invariants in a certain infinite family of ℤ_p-extensions. In the present article, we give analogous theorems in the case where k is a quartic CM-field. One of our main theorems determines all the Iwasawa invariants, including the ν-invariants, of a certain infinite family of ℤ_p-extensions over a quartic CM-field.

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