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.

References

↑ Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157, Ch. III, Exercise 8.3}}
↑ Vakil, Ravi (2007–2008), Foundations of algebraic geometry class 38 (PDF), Stanford University

This algebraic geometry–related article is a stub. You can help Wikipedia by adding missing information.

[1] Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157, Ch. III, Exercise 8.3}}

[2] Vakil, Ravi (2007–2008), Foundations of algebraic geometry class 38 (PDF), Stanford University

Projection formula

See also

References