Computing Néron–Severi groups and cycle class groups

@article{Poonen2015ComputingNG,
  title={Computing N{\'e}ron–Severi groups and cycle class groups},
  author={Bjorn Poonen and Damiano Testa and Ronald van Luijk},
  journal={Compositio Mathematica},
  year={2015},
  volume={151},
  pages={713 - 734}
}
Assuming the Tate conjecture and the computability of étale cohomology with finite coefficients, we give an algorithm that computes the Néron–Severi group of any smooth projective geometrically integral variety, and also the rank of the group of numerical equivalence classes of codimension $p$ cycles for any $p$. 
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Assuming the Tate conjecture and the computability of étale cohomology with finite coefficients, we give an algorithm that computes the Néron–Severi group of any smooth projective geometrically
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