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Representability of Chow groups of codimension three cycles
Published in De Gruyter Open Ltd
Volume: 22
Issue: 1
Pages: 127 - 134
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 l coefficients is zero and the second étale cohomology is spanned by divisors. We prove that then A3(X), the group of codimension three algebraically trivial cycles modulo rational equivalence, is dominated by finitely many copies of A0(S); this means that there exist finitely many correspondences Γi on S × X such that ςi Γi is surjective from A2(S) to A3(X). © 2022 Walter de Gruyter GmbH, Berlin/Boston.
About the journal
JournalAdvances in Geometry
PublisherDe Gruyter Open Ltd