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May 18, 2018 at 19:31 comment added Yonatan Harpaz Actually yes, thanks! If I understand correctly, it pretty much gives exactly what I wanted. So the proof boils down to the functoriality of the cycle class ${\rm Cl}(Z) \in H^2_Z(X,\mu_n)$. Also, I realized that the transversality condition is superfluous - it automatically holds in pullback squares of smooth schemes.
May 18, 2018 at 12:50 comment added Martin Bright Hi Yonatan, I think this is one of those things that is well known but nobody likes to prove. Does the top of p. 25 in arxiv.org/abs/1506.01817 help at all?
May 18, 2018 at 10:07 history edited Yonatan Harpaz CC BY-SA 4.0
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May 17, 2018 at 15:21 history asked Yonatan Harpaz CC BY-SA 4.0