Griffiths group

In mathematics, more specifically in algebraic geometry, the Griffiths group of a projective complex manifold "X" measures the difference between homological equivalence and algebraic equivalence, which are two important equivalence relations of algebraic cycles.
More precisely, it is defined as
where formula_2 denotes the group of algebraic cycles of some fixed codimension "k" and the subscripts indicate the groups that are homologically trivial, respectively algebraically equivalent to zero.
This group was introduced by Phillip Griffiths who showed that for a general quintic in formula_3 (projective 4-space), the group formula_4 is not a torsion group.