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Descent of coherent sheaves and complexes to geometric invariant theory quotients

Thomas Nevins
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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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Thomas Nevins. 2008-04-19. Descent of coherent sheaves and complexes to geometric invariant theory quotients. https://arxiv.org/abs/math/0206297

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