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In algebraic geometry, the projection formula states the following:http://math.stanford.edu/~vakil/0708-216/216class38.pdf For a morphism f:X\to Y of
ringed space In mathematics, a ringed space is a family of ( commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions. Precisely, it is a topological space equipped with a sheaf ...
s, an \mathcal_X-module \mathcal and a locally free \mathcal_Y-module \mathcal of finite rank, the natural maps of sheaves :R^i f_* \mathcal \otimes \mathcal \to R^i f_* (\mathcal \otimes f^* \mathcal) are isomorphisms. There is yet another projection formula in the setting of
étale cohomology In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conject ...
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See also

* Integration along fibers#Projection formula


References

Theorems in algebraic geometry {{algebraic-geometry-stub