Iwasawa module of the cyclotomic ℤ₂-extension of certain real quadratic fields

2024/10/22 by Avila, Josue
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2410.17458

openalex publication_date 2024/10/22 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

Abstract

For a real quadratic field K=ℚ(√(D)), let K_∞ denote the cyclotomic ℤ_p-extension of K. Greenberg conjectured that the corresponding Iwasawa module X_∞ is finite. Building on the work of Mouhib and Movahhedi, we provide new examples of real quadratic fields for which the conjecture holds, when X_∞ is cyclic and the prime is p=2. Furthermore, we find a fundamental system of units for certain biquadratic fields of the form ℚ(√(2), √(D)) and show how to use it to calculate the order of X_∞.

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