Greenberg's conjecture for real quadratic fields and the cyclotomic ℤ₂-extensions

2022/02/06 by Lorenzo Pagani, Pagani, Lorenzo
Computer Science · Mathematics · #11R29 #11Y40 (Primary) 11R23 (Secondary) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2202.02844

openalex publication_date 2022/02/06 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

Let A_n be the 2-part of the ideal class group of the n-th layer of the cyclotomic ℤ₂-extension of a real quadratic number field F. The cardinality of A_n is related to the index of cyclotomic units in the full group of units. We present a method to study the latter index. As an application we show that the sequence of the A_n's stabilizes for the real fields F=ℚ(√(f)) for any integer 0

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