An algebraic cycle on an algebraic variety 
is a finite
formal linear combination
![Z=sum_(i)n_i[Z_i],](/images/equations/AlgebraicCycle/NumberedEquation1.svg) |
where the 
are integers and the 
are irreducible closed subvarieties of
. A cycle of codimension 
has all its components of codimension 
(Stacks Project).
On a smooth projective complex algebraic variety, an algebraic cycle
of codimension 
defines a cohomology class
in 
of type 
,
hence a Hodge cycle (Deligne).
