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In the preprint arXiv:math/0505432v1 by Batyrev and Kreuser I have found (on pages 2 and 10) the claim that "by a recent result of Kresch and Vistoli [arXiv:math/0301249]" the (usual) Brauer group of a Calabi-Yau threefold is isomorphic to its cohomological Brauer group. However, in that preprint of Kresch and Vistoli I have not found a word about Calabi-Yau or anything. (Admittedly, it is about Brauer groups). Could anyone help me to clear the mess?

P.S. For what I know, if there is always an isomorphism is a big open problem which is only settled in a few special cases. So, I suppose, if this is known indeed for Calabi-Yau threefolds (for 10 years by now), then every expert must be aware of it.

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It follows from a theorem of Gabber that for any quasi-projective variety the usual Brauer group is equal to the cohomological Brauer group. See, for example math.columbia.edu/~dejong/papers/2-gabber.pdf –  ulrich Oct 5 '12 at 13:13
Thank you for the reference –  Alex Gavrilov Oct 6 '12 at 14:22
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up vote 4 down vote accepted

It was proved by Gabber and De Jong that the cohomological Brauer group of a quasi-compact scheme with an ample invertible sheaf equals its Brauer group. Our preprint does not contain this result.

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