ScalingStacks

Remark 1.3. The hypothesis that our stacks are perfect appears to be essential, and we do not expect the above theorem to hold in significantly greater generality. Alternatively, in complete generality, one should rather replace the notion of tensor product. Jacob Lurie has described (in private communication) a completed tensor product for stable $\infty$-categories equipped with $t$-structures, and such that passing to quasi-coherent sheaves takes fiber products of geometric stacks to the completed tensor product of $\infty$-categories.