Galois descent of equivalences between blocks of $p$-nilpotent groups

We give sufficient conditions on $p$-blocks of $p$-nilpotent groups over ${\mathbb{F}}_p$ to be splendidly Rickard equivalent and $p$-permutation equivalent to their Brauer correspondents. The paper also contains Galois descent results on $p$-permutation modules and $p$-permutation equivalences that hold for arbitrary groups.