Cohomology Of A Stack - Wikipedia

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iconThis article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: "Cohomology of a stack" – news · newspapers · books · scholar · JSTOR (March 2020) (Learn how and when to remove this message)

In algebraic geometry, the cohomology of a stack is a generalization of étale cohomology. In a sense, it is a theory that is coarser than the Chow group of a stack.

The cohomology of a quotient stack (e.g., classifying stack) can be thought of as an algebraic counterpart of equivariant cohomology. For example, Borel's theorem states that the cohomology ring of a classifying stack is a polynomial ring.

See also

[edit]
  • l-adic sheaf
  • smooth topology

References

[edit]
  • Gaitsgory, Dennis; Lurie, Jacob (2019), Weil's Conjecture for Function Fields (PDF), Annals of Mathematics Studies, vol. 199, Princeton, NJ: Princeton University Press, MR 3887650
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Tag » Cohomology Of Quotient Stacks