On degenerate CM-types
type: Item
instance of: scholarly article
title: On degenerate CM-types
zbMATH Open document ID: 0814.11052
author: Hiromichi Yanai
published in: Journal of Number Theory
publication date: 1995-06-18T00:00:00Z
review text: Let \(K\) be a CM-field of degree \(2d\) and let \(\Gamma_ K\) denote the set of embeddings of \(K\) into \(\mathbb{C}\). A subset \(S\) of \(\Gamma_ K\) is called a CM-type if \(S \bigcup S\rho = \Gamma_ K\) and \(S \bigcap S\rho = \emptyset\), where \(\rho\) denotes the complex conjugation. The rank of \(S\) was defined by \textit{T. Kubota} [Trans. Am. Math. Soc. 118, 113-122 (1965; Zbl 0146.279)] in order to study the abelian extensions obtained by complex multiplication. Let \(A\) be an abelian variety with complex multiplication of type \((K,S)\). Then \(\dim A = d\) and \(\text{rank }S \leq d + 1\). If \(\text{rank }S < d + 1\), then \(S\) is called degenerate. The author gives a method of constructing degenerate CM-types systematically. He also investigates the fields of moduli for such CM-types.
Mathematics Subject Classification ID: 11R20
Mathematics Subject Classification ID: 11G15
zbMATH DE Number: 710372
zbMATH Keywords: Hodge group
zbMATH Keywords: CM-field
zbMATH Keywords: complex multiplication
zbMATH Keywords: abelian variety
zbMATH Keywords: degenerate CM-type
zbMATH Keywords: fields of moduli
reviewed by: Veikko Ennola
MaRDI profile type: Publication
full work available at URL: jnth.1994.1095
OpenAlex ID: W1514049892
DOI: 10.1006/JNTH.1994.1095
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description: scientific article; zbMATH DE number 710372