In
algebraic geometry, the projection formula states the following:
[http://math.stanford.edu/~vakil/0708-216/216class38.pdf ]
For a morphism
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 of ...
s, an
-module
and a
locally free -module
of finite rank, the natural maps of sheaves
:
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 conjectur ...
.
See also
*
Integration along fibers#Projection formula
References
Theorems in algebraic geometry
{{algebraic-geometry-stub