Descent of splendid Rickard equivalences in ${\mathrm{GL}}_n(q)$

Xin Huang, Pengcheng Li, Jiping Zhang

Let $n$ be a positive integer and $q$ a prime power. We prove that a refined version of Broué's abelian defect group conjecture holds for unipotent $\ell$-blocks of ${\mathrm{GL}}_n(q)$…