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Fermat Jacobians of Prime Degree over Finite Fields

  Published:1999-03-01
 Printed: Mar 1999
  • Josep Gonz├ílez
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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, 14H40 show english descriptions Curves over finite and local fields [See also 14H25]
Jacobians, Prym varieties [See also 32G20]
11G20 - Curves over finite and local fields [See also 14H25]
14H40 - Jacobians, Prym varieties [See also 32G20]
 

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