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Aug 26, 2016 at 14:38 comment added Olivier Benoist As I was indicated by Totaro, the case of abelian threefolds has been answered positively by Craig Grabowski in his thesis "On the integral Hodge conjecture for $3$-folds".
Oct 24, 2012 at 17:21 answer added J.C. Ottem timeline score: 6
Oct 24, 2012 at 17:03 comment added Matt The integral Hodge conjecture is known to be false for Calabi-Yau 3-folds. See Kollar's "Classification of Irregular Varieties" or Voisin's "On integral Hodge classes on uniruled or Calabi-Yau threefolds."
Oct 24, 2012 at 16:58 history edited 喻yuwei CC BY-SA 3.0
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Oct 24, 2012 at 16:27 comment added diverietti I think we don't even know for abelian varieties...
Oct 24, 2012 at 16:00 history asked 喻yuwei CC BY-SA 3.0