equivariant derived category

Equivariant derived categories


Given a locally compact group GG and a GG-space XX, one can consider the category of GG-equivariant sheaves on XX. It has been understood by Joseph Bernstein and Valery Lunts that the derived category of the abelian category of equivariant sheaves (or of any other abelian category) is not the most sensible choice, when the action is not free and GG is not discrete. Instead one needs to use GG-resolutions, i.e. to effectively consider resolutions of the space XX itself while defining the derived category.


  • J. Bernstein, V. Lunts, Equivariant sheaves and functors, Springer Lecture Notes in Math. 1578 (1994). MR95k:55012
  • notes by Zhiwei Yun, pdf
  • Masaki Kashiwara, Equivariant derived category and representation of real semisimple Lie groups, pdf

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