Field of moduli versus field of definition for cyclic covers of the projective line

Kontogeorgis, Aristides

Journal de théorie des nombres de Bordeaux, Tome 21 (2009) no. 3, pp. 679-693.

Nous donnons un critère, dépendant du groupe des automorphismes, pour que certains revêtements cycliques de la droite projective soient définis sur leur corps de modules. Nous donnons aussi un exemple de revêtement cyclique de la droite projective complexe de corps de module $ℝ$ qui ne peut pas être défini sur $ℝ$.

$$ We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli $ℝ$ that can not be defined over $ℝ$ is also given.

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