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equivariant derived category

Equivariant derived categories

Equivariant derived categories

Idea

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.

References

  • 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

  • Geoff Vooys, Equivariant Functors and Sheaves (arXiv:2107.01778)

Last revised on October 5, 2021 at 05:30:19. See the history of this page for a list of all contributions to it.