  We strengthen the results of Boltje and Yilmaz regarding the Galois descent
of equivalences of blocks of $p$-nilpotent groups and a result of Kessar and
Linckelmann regarding Galois descent of splendid Rickard equivalences for
blocks with compatible Galois stabilizers. A more general descent criteria for
chain complexes is proven along the way, which requires the adaptation of a
theorem of Reiner for chain complexes. This verifies Kessar and Linckelmann's
refinement of Brou\'{e}'s abelian defect group conjecture for blocks of
$p$-nilpotent groups with abelian Sylow $p$-subgroup.
