Derived equivalence of DG algebras from derived equivalence of their cohomology rings

Determine whether, for cochain differential graded algebras A and B, a derived equivalence between the graded cohomology rings H(A) and H(B) implies that the differential graded algebras A and B are themselves derived equivalent.

Background

Dugas raised the question of whether derived equivalence of cohomology rings forces derived equivalence of the underlying differential graded (DG) algebras. Pan, Peng, and Zhang constructed specific DG endomorphism algebras whose cohomology rings are derived equivalent, yielding affirmative results in certain special cases.

The present paper constructs explicit DG free algebras A1 and A2 with isomorphic cohomology rings but non-isomorphic derived Picard groups, thereby showing that derived equivalence of cohomology rings does not imply derived equivalence of the DG algebras in general. This provides a negative answer to the question posed by Dugas.