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arXiv · 1206.4179

Cohomology and base change for algebraic stacks

Jack Hall
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Abstract

We prove that cohomology and base change holds for algebraic stacks, generalizing work of Brochard in the tame case. We also show that Hom-spaces on algebraic stacks are represented by abelian cones, generalizing results of Grothendieck, Brochard, Olsson, Lieblich, and Roth--Starr. To accomplish all of this, we prove that a wide class of Ext-functors in algebraic geometry are coherent (in the sense of M. Auslander).

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Jack Hall. 2013-03-15. Cohomology and base change for algebraic stacks. https://arxiv.org/abs/1206.4179

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