Duality relating spaces of algebraic cocycles and cycles

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(s)H(k)(X) --> L(n-s)H(2n-k)(X) for 2s less than or equal to k which carry over via natural transformations to the Poincare duality isomorphism H-k(X;Z) --> H-2n-k(X;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 x Y is a weak homotopy equivalence. The main results have a wide variety of applications. Among these are the determination of the homotopy type of certain algebraic mapping complexes and a computation of the group of algebraic s-cocycles module algebraic equivalence on a smooth projective variety. Copyright (C) 1996 Elsevier Science Ltd