### Duality Relating Spaces of Algebraic Cocycles and Cycles, by Eric M. Friedlander and H. Blaine Lawson

In this paper a fundamental duality is established between algebraic cycles
and algebraic cocycles on a smooth projective variety. The proof makes use
of a new Chow moving lemma for families. If $X$ is a smooth projective
variety of dimension $n$, our duality map induces isomorphisms $L^sH^k(X) \to
L_{n-s}H_{2n-k}(X)$ for $2s\leq k$ which carry over via natural
transformations to the Poincar\'e duality isomorphism $H^k(X;{\bf Z}) \to
H_{2n-k}(X;{\bf Z})$. More generally, for smooth projective varieties $X$
and $Y$ the natural graphing homomorphism sending algebraic cocycles on $X$
with values in $Y$ to algebraic cycles on the product $X\times Y$ is a weak
homotopy equivalence. Among applications presented are the determination of
the homotopy type of certain algebraic mapping complexes and a computation of
the group of algebraic $s$-cocycles modulo algebraic equivalence on a smooth
projective variety.

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

H. Blaine Lawson <blawson@sbccmail.edu>