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Apr 28 at 21:48 comment added user267839 @WillSawin: Right, beeing sheaf of Abelian groups is neccessary to have enough injectives to resolve so far I understand. Yes sorry, I overlooked, in Kiehl & Freitag's EC it's Thm 8.9, and another source rather nice elaborating this is Lei Fu's ECT, Cor 7.8.3.
Apr 28 at 14:10 comment added Will Sawin Abelian group structure is needed just to define the higher direct images. And doesn't the answer you linked include a reference to the result?
Apr 28 at 13:14 history edited user267839 CC BY-SA 4.0
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Apr 28 at 12:17 history asked user267839 CC BY-SA 4.0