A note on algebraic \(\Gamma\)-monomials and double coverings
type: Item
instance of: scholarly article
title: A note on algebraic \(\Gamma\)-monomials and double coverings
zbMATH Open document ID: 1010.11060
author: Soogil Seo
published in: Journal of Number Theory
publication date: 2002-06-11T00:00:00Z
review text: We discuss algebraic \(\Gamma\)-monomials of Deligne. Deligne used the theory of Hodge cycles to show that algebraic \(\Gamma\)-monomials generate Kummer extensions of certain cyclotomic fields. \textit{P. Das} [Trans. Am. Math. Soc. 352, 3557-3594 (2000; Zbl 1013.11069)], using a double complex of Anderson and Deligne's results, showed that certain powers of algebraic \(\Gamma\)-monomials and certain square roots of sine monomials generate abelian extensions of \(\mathbb{Q}\). Das also gave one example of a nonabelian double covering of a cyclotomic field generated by the square root of a sine monomial. In this note, we will produce infinitely many examples of nonabelian double coverings of cyclotomic fields of Das type. The construction of the examples depends in an interesting way on a lemma of Gauss figuring in an elementary proof of quadratic reciprocity.
reviewed by: Florence Soriano-Gafiuk
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R32
zbMATH DE Number: 1753719
MaRDI profile type: Publication
full work available at URL: jnth.2001.2714
OpenAlex ID: W2076724557
cites work: Q4227232
cites work: Algebraic gamma monomials and double coverings of cyclotomic fields
cites work: Q3895546
cites work: Hodge cycles, motives, and Shimura varieties
cites work: The universal ordinary distribution
cites work: The Z/2 Z cohomology of the universal ordinary distribution
cites work: Q3995821
cites work: On the Stickelberger ideal and the circular units of a cyclotomic field
cites work: Q3943047
DOI: 10.1006/JNTH.2001.2714
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description: scientific article; zbMATH DE number 1753719