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Fermat Jacobians of Prime Degree over Finite Fields
Published online by Cambridge University Press: 20 November 2018
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.
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- Copyright © Canadian Mathematical Society 1999
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