Abstract
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.
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