Computing N\'eron-Severi groups and cycle class groups
  Assuming the Tate conjecture and the computability of \'etale cohomology with finite coefficients, we give an algorithm that computes the N\'eron-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. 
Bjorn Poonen, Damiano Testa, and Ronald van Luijk
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