Motives of Uniruled 3-Folds

Abstract

J. Murre has conjectured that every smooth projective variety X of dimension d admits a decomposition of the diagonal δ=p $_0$ +…+p $_2d$ ∈ CH $^d$ (X × X) [otimes ] Q such that the cycles p $_i$ are orthogonal projectors which lift the Künneth components of the identity map in étale cohomology. If this decomposition induces an intrinsic filtration on the Chow groups of X, we call it a Murre decomposition. In this paper we propose candidates for such projectors on 3-folds by using fiber structures. Using Mori theory, we prove that every smooth uniruled complex 3-fold admits a Murre decomposition.