Keller’s generation conjecture for finite-dimensional algebras

Prove that for every finite-dimensional algebra A over a field k, the k-linear dual A^\vee = Hom_k(A,k) generates the unbounded derived dg category Mod_A of right A-modules.

Background

The paper situates its counterexample within the family of homological conjectures for finite-dimensional algebras. Keller’s conjecture asserts generation of the unbounded derived category by the dualizing module A\vee. The paper disproves a broader proposed analogue for all dg algebras with finite-dimensional cohomology, but does not resolve Keller’s conjecture for ordinary finite-dimensional algebras.

References

Keller's strong form of the homological conjectures asserts: any finite dimensional algebra cogenerates its unbounded derived category of modules.

— A proper dg algebra which does not cogenerate  (2609.34193 - Hu et al., 28 Sep 2026) in Conjecture 1, Section 1 (Introduction)

We are not aware of a proper connective dg algebra that does not cogenerate its module category.

— A proper dg algebra which does not cogenerate  (2609.34193 - Hu et al., 28 Sep 2026) in Remark following Section \ref{sec: example dga}