Descent of coherent sheaves and complexes to geometric invariant theory quotients

Thomas Nevins

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)2481-2495
Number of pages15
JournalJournal of Algebra
Volume320
Issue number6
DOIs
StatePublished - Sep 15 2008

Keywords

  • Derived categories
  • Descent
  • Geometric invariant theory

ASJC Scopus subject areas

  • Algebra and Number Theory

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