An algebraic correspondence between algebraic varieties 
and 
is an algebraic cycle on their product 
. For smooth projective complex varieties, a codimension-
correspondence 
acts on rational cohomology by
 |
where 
and 
are the projections and 
is the cycle class. It sends 
to 
, with the corresponding Tate
twist for Hodge structures. The graph of a
morphism is an example. Realizing a particular cohomological map by such a cycle
is stronger than merely knowing that the map preserves Hodge types.
