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Fermat Jacobians of Prime Degree over Finite Fields

Published online by Cambridge University Press:  20 November 2018

Josep González
Josep González*
Affiliation:
Escola Universitària Politècnica de Vilanova i la Geltrú Departament de Matemàtica Aplicada i Telemàtica Av. Victor Balaguer s/n Vilanova i la Geltrú 08800 Spain, e-mail: josepg@mat.upc.es
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Abstract

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We study the splitting of Fermat Jacobians of prime degree $\ell $ over an algebraic closure of a finite field of characteristic $p$ not equal to $\ell $. We prove that their decomposition is determined by the residue degree of $p$ in the cyclotomic field of the $\ell $-th roots of unity. We provide a numerical criterion that allows to compute the absolutely simple subvarieties and their multiplicity in the Fermat Jacobian.

Keywords

11G2014H40
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 1 , 01 March 1999 , pp. 78 - 86
Copyright
Copyright © Canadian Mathematical Society 1999

References

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