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Apr 30, 2015 at 15:24 comment added Amit H The correct analogue of 1) would be $H^{p,q}(X,{\mathbb Z})=0$ when $p>q+cd(X)+1$ where $cd(X)$ is the etale cohomological dimension of $X$ (in the Nisnevich case, this agrees with dim(X)) and the +1 has to do with the fact that the sheaves may not be torsion.
Apr 15, 2015 at 8:29 vote accept Carlos
Apr 14, 2015 at 14:42 history answered Matthias Wendt CC BY-SA 3.0