Projection formula

In algebraic geometry, the projection formula states that,[1][2] for a quasi-compact separated morphism of schemes f:X \to Y, a quasi-coherent sheaf \mathcal{F} on X, a locally free sheaf \mathcal{E} on Y, the natural maps of sheaves

R^i f_* \mathcal{F} \otimes \mathcal{E} \to R^i f_* (\mathcal{F} \otimes f^* \mathcal{E})

are isomorphisms.

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

See also

References

  1. ↑ Hartshorne 1977, Ch III, Exercise 8.3
  2. ↑ http://math.stanford.edu/~vakil/0708-216/216class38.pdf

Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157 


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