Affiliation:
1. Harish Chandra Research Institute , Allahabad India
Abstract
Abstract
Assume that we have a fibration of smooth projective varieties X → S over a surface S such that X is of dimension four and that the geometric generic fiber has finite-dimensional motive and the first étale cohomology of the geometric generic fiber with respect to ℚ
l
coefficients is zero and the second étale cohomology is spanned by divisors. We prove that then A
3(X), the group of codimension three algebraically trivial cycles modulo rational equivalence, is dominated by finitely many copies of A
0(S); this means that there exist finitely many correspondences Γi
on S × X such that Σ
i Γi
is surjective from A
2(S) to A
3(X).
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