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

• l-adic sheaf
• smooth topology

References

• 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