Charles mentioned this. There is some kind of operator, perhaps a power of the Lefschetz operator, going from to or something like that. The kernel of this is called primitive cohomology, apparently.
arXiv: Experimental full text search
AG (Algebraic geometry)
Pure
This term probably refers to the pieces of a Weil cohomology occurring in the “primitive decomposition” induced by a Lefschetz operator. See André, chapter 5, and Weil cohomology.
http://mathoverflow.net/questions/14667/intuition-for-primitive-cohomology
nLab page on Primitive cohomology