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# Fermat Jacobians of Prime Degree over Finite Fields

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Published:1999-03-01
Printed: Mar 1999
• Josep González
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## Abstract

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.
 MSC Classifications: 11G20 - Curves over finite and local fields [See also 14H25] 14H40 - Jacobians, Prym varieties [See also 32G20]

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