${\bf C}^*$-extensions of tori, higher Chow groups and applications to incidence equivalence relations for algebraic cycles.

Details ${\bf C}^*$-extensions of tori, higher Chow groups and applications to incidence equivalence relations for algebraic cycles. ${\bf C}^*$-extensions of tori, higher Chow groups and applications to incidence equivalence relations for algebraic cycles.

1995-01-10

arxiv.org/abs/alg-geom/9501004v2

Mathematics

Algebraic Geometry

14 pages, Latex2e, no figures

Scientific paper

Let X be a smooth projective variety of dimension n. If $p+q=n+1$ then Bloch has defined a ${\bf G}_m$-biextension E over the product of the Chow groups $CH^p_0(X)$ and $CH^q_0(X)$ of homologically trivial cycles. We prove that E is the pullback of the Poincare biextension over the product of intermediate Jacobians in characteristic zero. This is used to study various equivalence relations for algebraic cycles. In particular we reprove Murres result that Griffiths conjecture holds for codimension two cycles, i.e. every codim. two cycle algebraically and incidence equivalent to zero has torsion Abel-Jacobi invariant.

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