On decomposition numbers and Alvis-Curtis duality

We show that for general linear groups ${\mathrm{G}\mathrm{L}}_n(q)$ as well as for $q$-Schur algebras the knowledge of the modular Alvis-Curtis duality over fields of characteristic $\mathrm{\ell }$, $\mathrm{\ell }\nmid q$, is equivalent to the knowledge of the decomposition numbers.