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Allen Knutson said here in comments below the question that I generally regard torsion in (co)homology as a sign that one should be computing K-theory instead, which has less of it. I know one ...

I have a question about the equivalence of derived categories. Let $\mathcal{A} = \mathcal{A}'\oplus \mathcal{A}''$ and $\mathcal{B} = \mathcal{B}' \oplus \mathcal{B}''$ are direct sum of abelian ...