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Mar 11, 2020 at 5:49 comment added abx Now Theorem 1.4 in Deligne's Exposé 19 gives you the best general result you can hope for.
Mar 11, 2020 at 5:38 comment added Jana @abx Thank you, I have edited the question by replacing $\mathbb{Z}$ by $\mathbb{Q}$.
Mar 11, 2020 at 5:37 history edited Jana CC BY-SA 4.0
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Mar 11, 2020 at 5:28 comment added abx The question would make more sense with $\Bbb{Z}$ replaced by $\Bbb{Q}$; then the answer (for the last question) would be positive, with some exceptions. See Deligne's Exposé 19 in SGA 7.
Mar 11, 2020 at 4:45 answer added Nick L timeline score: 2
Mar 11, 2020 at 3:57 history asked Jana CC BY-SA 4.0