preprint Igor Burban author 72064 Daniel Perniok author 64242 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 eng 2608.24331 Burban, Igor, and Daniel Perniok. <i>Double Hall Algebras and Derived Equivalences Revisited</i>. 2026. Burban I, Perniok D. Double Hall algebras and derived equivalences revisited. Published online 2026. @article{Burban_Perniok_2026, title={Double Hall algebras and derived equivalences revisited}, author={Burban, Igor and Perniok, Daniel}, year={2026} } Burban, I., &#38; Perniok, D. (2026). <i>Double Hall algebras and derived equivalences revisited</i>. I. Burban and D. Perniok, “Double Hall algebras and derived equivalences revisited.” 2026. Burban, Igor, and Daniel Perniok. “Double Hall Algebras and Derived Equivalences Revisited,” 2026. I. Burban, D. Perniok, (2026). 668592026-08-26T12:08:41Z2026-08-26T12:15:11Z