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arXiv · 2508.17574

Derived equivalences of DG algebras are not governed by their cohomology rings

X. -F. Mao·R. -K. Lu
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Abstract

Let $\mathscr{A}$ and $\mathscr{B}$ be two connected cochain DG algebra such that $\mathscr{A}^{\#}=\mathscr{B}^{\#}$ and the cohomology rings $H(\mathscr{A})$ and $H(\mathscr{B})$ are isomorphic. We give examples to show that $\mathscr{A}$ and $\mathscr{B}$ are not necessarily derived equivalent, thereby answering to a question of Dugas.

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X. -F. Mao, R. -K. Lu. 2025-08-25. Derived equivalences of DG algebras are not governed by their cohomology rings. https://arxiv.org/abs/2508.17574

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