### Chow Motives of 3-folds and Fiber Spaces, by Pedro L. del Angel and Stefan J. Mueller-Stach

Let k be a field of characteristic zero. For every smooth projective
k-variety Y of dimension n which admits a proper, connected morphism f of
relative dimension one onto a smooth projective k-variety S, we construct
idempotent correspondences (projectors) in the product of Y with itself,
i.e. pure Chow motives in the sense of Grothendieck. If n=3 and a precise
condition on the second cohomology group of Y is satisfied, we can prove
that there exists a Chow-Kuenneth decomposition of the diagonal on Y
(Murre's Conjecture). We give examples, even 3-folds of general type,
where our method applies.

Pedro L. del Angel <plar@xanum.uam.mx>

Stefan J. Mueller-Stach <mueller-stach@uni-essen.de>