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.
