Descent of coherent sheaves and complexes to geometric invariant theory quotients

2002/06/27 by Thomas Nevins, Nevins, Thomas
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.math/0206297

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.

Related

• On the structure of equivariant derived categories
• The derived category of a GIT quotient
• Perverse coherent sheaves (after Deligne)
• New enhancements of derived categories of coherent sheaves and\n applications
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