An algebraic correspondence between two varieties, $V,W$ is a kind of multi-valued map from $V$ to $W$, or, in other words, a map from a covering $U$ of $V$ to $W$. Apparently, such a map gives a morphism from the cohomology of $W$ to that of $V$. How does this work? I know that we would get a map to the cohomology of $U$, by the functorial nature of cohomology. However, how do we then map this to an element of the cohomology of $V$?
Topological description of map coming from correspondence
0
$\begingroup$
algebraic-geometry
algebraic-topology
intersection-theory