Chow Motives of 3-folds and Fiber Spaces
نویسنده
چکیده
Let k be a field of characteristic zero. For every smooth, projective k-variety Y of dimension n which admits a connected, proper morphism f : Y → S of relative dimension one, we construct idempotent correspondences (projectors) πij(Y ) ∈ CH (Y × Y,Q) generalizing a construction of Murre. If n = 3 and the transcendental cohomology group H tr(Y ) has the property that H tr(Y,C) = f H tr(S,C) + Im(f H(S,C) ⊗ H(Y,C) → H tr(Y,C)), then we can construct a projector π2(Y ) which lifts the second Künneth component of the diagonal of Y . Using this we prove that many smooth projective 3-folds X over k admit a Chow-Künneth decomposition ∆ = p0 + ... + p6 of the diagonal in CH (X × X,Q).
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