### Filtrations on algebraic cycles and homology, by Eric M. Friedlander

As shown by the author and B. Mazur, Lawson homology theory determines
natural filtrations on algebraic equivalence classes of algebraic cycles and
on the singular integral homology groups of complex projective varieties. In
this paper, the filtration on cycles is identified in terms of the images
under correspondences of cycles homologically equivalent to zero. This is
closely related to a filtration recently introduced by M. Nori. The author
and B. Mazur conjectured that the filtration on (rational) homology groups
was equal to the "geometric (or level) filtration" introduced by
A. Grothendieck. It is shown here that this conjecture is implied by the
validity of Grothendieck's Conjecture B. Both filtrations can be interpreted
in terms of a spectral sequence whose various terms have a motivic nature.

The two central constructions of the paper are the s-map (introduced by
the author and B. Mazur) and the graph mapping. Various equivalent
descriptions of the s-map are presented and some of its basic properties are
verified. The graph mapping is an elementary construction on cycle spaces
which enables one to extend classical constructions involving correspondences
to singular varieties.

Eric M. Friedlander <eric@math.nwu.edu>