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Hodge cycles on the jacobian variety of the Catalan curve

Published online by Cambridge University Press:  04 December 2007

FUMIO HAZAMA
FUMIO HAZAMA
Affiliation:
Department of Information Sciences, College of Science and Engineering Tokyo Denki University, Hatoyama, Hiki-gun, Saitama 350-03, Japan
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Abstract

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The jacobian variety of the Catalan curve $y^q = x^p - 1$ is shown to be nondegenerate. As an application, a 0-1-matrix whose determinant computes the relative class number of the $pq$-th cyclotomic field is constructed.

Keywords

Catalan curveHodge groupclass number
Type
Research Article
Information
Compositio Mathematica , Volume 107 , Issue 3 , July 1997 , pp. 339 - 353
Copyright
© 1997 Kluwer Academic Publishers