On a smooth projective variety X of dim n with dualising sheaf ωₓ: Hⁱ(X,F)* ≅ Hⁿ⁻ⁱ(X, F* ⊗ ωₓ). Specializes to Poincaré duality.
On a smooth projective variety X of dim n with dualising sheaf ωₓ: Hⁱ(X,F)* ≅ Hⁿ⁻ⁱ(X, F* ⊗ ωₓ). Specializes to Poincaré duality.