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An associative algebra $A$ is said to be Morita equivalent to another one $B$ if there is an equivalence $$\mathsf{Mod}_A\simeq \mathsf{Mod}_B$$ between its corresponding abelian categories of modules. Moreover, whenever $A$ and $B$ are commutative, they are Morita equivalent iff they are isomorphic. On the other hand, we say that $A$ is derived Morita equivalent to $B$ if there is an equivalence $$D(A)\simeq D(B)$$ between its triangulated derived categories. My question is:

Q. If $A$ is commutative and derived Morita equivelent to $B$, is $A$ Morita equivalent to $B$?

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This seems to be true by https://arxiv.org/pdf/math/9810134.pdf , theorem 2.7.

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