Cohomology of a stack
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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
References
- {{citation|first1=Dennis|last1=Gaitsgory|author1-link=Dennis Gaitsgory| first2=Jacob|last2= Lurie |author2-link=Jacob Lurie| title=Weil's Conjecture for Function Fields|url=http://www.math.harvard.edu/~lurie/papers/tamagawa.pdf|series=Annals of Mathematics Studies|volume= 199|publisher= Princeton University Press |location= Princeton, NJ|year= 2019|mr=3887650}}
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