Hodge loci and absolute Hodge classes

@article{Voisin2007HodgeLA,
  title={Hodge loci and absolute Hodge classes},
  author={Claire Voisin},
  journal={Compositio Mathematica},
  year={2007},
  volume={143},
  pages={945 - 958}
}
  • C. Voisin
  • Published 30 May 2006
  • Mathematics
  • Compositio Mathematica
This paper addresses several questions related to the Hodge conjecture. First of all we consider the question, asked by Maillot and Soulé, whether the Hodge conjecture can be reduced to the case of varieties defined over number fields. We show that this is the case for the Hodge classes whose corresponding Hodge locus is defined over a number field. We also give simple criteria for this last condition to be satisfied. Finally we discuss the relation between this condition and the notion of… 
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