From Wikipedia, the free encyclopedia
In
algebraic geometry, the projection formula states the following:
[1]
[2]
For a morphism
of
ringed spaces, an
-module
and a
locally free
-module
of finite rank, the natural maps of sheaves
![{\displaystyle R^{i}f_{*}{\mathcal {F}}\otimes {\mathcal {E}}\to R^{i}f_{*}({\mathcal {F}}\otimes f^{*}{\mathcal {E}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/53a19802e24c313f37bdaa3880a1c386ddcb4ac8)
are isomorphisms.
There is yet another projection formula in the setting of
étale cohomology.
-
^
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