# Projection formula

In algebraic geometry, the **projection formula** states that,[1][2] for a quasi-compact separated morphism of schemes , a quasi-coherent sheaf on *X*, a locally free sheaf on *Y*, the natural maps of sheaves

are isomorphisms.

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

## References

- Hartshorne 1977, Ch III, Exercise 8.3
- 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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