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A Note on Algebraic Γ-Monomials and Double Coverings

✍ Scribed by Soogil Seo

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
112 KB
Volume
93
Category
Article
ISSN
0022-314X

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✦ Synopsis

We discuss algebraic C-monomials of Deligne. Deligne used the theory of Hodge Cycles to show that algebraic C-monomials generate Kummer extensions of certain cyclotomic fields. Das, using a double complex of Anderson and Deligne's results, showed that certain powers of algebraic C-monomials and certain square roots of sine monomials generate abelian extensions of 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.

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