Standardness of derived equivalences between algebras

Determine whether every k-linear triangulated equivalence between the unbounded derived categories of modules over associative algebras A and B is of standard type; specifically, show that any exact k-linear triangulated equivalence F: D(Mod A) -> D(Mod B) is functorially isomorphic to the derived tensor product - ⊗^L_A M for some complex M of A–B-bimodules.

Background

Rickard’s Derived Morita Theorem characterizes when derived categories of algebras are equivalent and shows that many such equivalences arise from tilting complexes. A natural expectation is that all derived equivalences between module categories over algebras should be of the ‘standard’ form induced by derived tensoring with a complex of bimodules, analogously to Eilenberg–Watts in the abelian setting.

However, a general derived Eilenberg–Watts theorem for triangulated categories fails because the relevant functor categories are not triangulated. While the dg-enhanced setting resolves this via Toën’s derived Eilenberg–Watts theorem, the question remains open for ordinary derived categories of algebras.