  Fix a scheme $X$ over a field of characteristic zero that is equipped with an
action of a reductive algebraic group $G$.
  We give necessary and sufficient conditions for a $G$-equivariant coherent
sheaf on $X$ or a bounded-above complex of $G$-equivariant coherent sheaves on
$X$ to descend to a good quotient $X//G$. This gives a description of the
coherent derived category of $X//G$ as an admissible subcategory of the
equivariant derived category of $X$.
