Descent of coherent sheaves and complexes to geometric invariant theory quotients

Details Descent of coherent sheaves and complexes to geometric invariant theory quotients Descent of coherent sheaves and complexes to geometric invariant theory quotients

2002-06-27

arxiv.org/abs/math/0206297v3

Mathematics

Algebraic Geometry

substantially revised

Scientific paper

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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