Rickard's standardness conjecture for derived equivalences of flat algebras

Let AA and BB be flat algebras. A derived equivalence is a functor

D(A-Mod)D(B-Mod).\mathbf{D}(A\text{-}{\rm Mod})\longrightarrow \mathbf{D}(B\text{-}{\rm Mod}).

It is standard when it is induced by tensoring with a complex of bimodules in the usual derived sense.

Rickard's conjecture. Any derived equivalence between flat algebras is standard.

This is described as the unbounded version of an open question raised by Rickard. The paper proves that, for flat algebras, standard and canonical derived equivalences are equivalent, but the conjecture itself is not reported as resolved here.

Sources & referencesView supporting material

Primary source

Xiao-Wu Chen, “Pre-weight structures, pseudo-identities and canonical derived equivalences”, arXiv:2311.08044 (2023).

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