Imaginary logarithmic classes of abelian number fields

2024/06/27 by Jean-François Jaulent, Jaulent, Jean-François
Mathematics · #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2406.18929

Abstract

We are interested in classical and logarithmic imaginary classes of abelian number fields in connection with Iwasawa theory. For any given odd prime ℓ and any imaginary abelian number field K, we compute the isotypic components of the logarithmic ℓ-class group of K associated to imaginary irreducible ℓ-adic characters of its Galois group and we extend to this situation the Gold criterium on lambda invariants. We first study the semi-simple case, thus the non semi-simple case in connection with transition formulas of genus for supercircular fields.

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