Projection formula

In algebraic geometry, the projection formula states the following:

For a morphism $f:X\to Y$ of ringed spaces, an ${𝒪}_X$-module $ℱ$ and a locally free ${𝒪}_Y$-module $ℰ$ of finite rank, the natural maps of sheaves

$R^i{f}_{*}ℱ\otimes ℰ\to R^i{f}_{*}(ℱ\otimes f^{*}ℰ)$

are isomorphisms.

There is yet another projection formula in the setting of étale cohomology.

See also

• Integration along fibers § Projection formula