Double Hall algebras and derived equivalences revisited Burban, Igor Perniok, Daniel Let $\mathbb{k}$ be a finite field and $\mathcal{A}, \mathcal{B}$ be $\mathbb{k}$-linear $\mathsf{Ext}$-finite hereditary abelian categories. A theorem of Cramer asserts that, under suitable assumptions, a derived equivalence $\mathcal{D}^b(\mathcal{A}) \!\longrightarrow\! \mathcal{D}^b(\mathcal{B})$ between two such categories induces an algebra isomorphism of the corresponding double Hall algebras $\mathsf{DH}_\mathcal{A} \!\longrightarrow\! \mathsf{DH}_\mathcal{B}$. It turns out that a counting formula for certain distinguished triangles in $\mathcal{D}^b(\mathcal{A})$, on which Cramer's proof relies, is incorrect in general. We give a corrected proof of Cramer's theorem which preserves the overall strategy of his approach. 2026 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://ris.uni-paderborn.de/record/66859 Burban I, Perniok D. Double Hall algebras and derived equivalences revisited. Published online 2026. eng info:eu-repo/semantics/altIdentifier/arxiv/2608.24331 info:eu-repo/semantics/closedAccess