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

Stefan Müller-Stach

paper

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

arXiv:alg-geom/9501004

Abstract

Let X be a smooth projective variety of dimension n. If $p + q = n + 1$ then Bloch has defined a $G_{m}$ -biextension E over the product of the Chow groups $C H_{0}^{p} (X)$ and $C H_{0}^{q} (X)$ 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.

arXiv comment14 pages, Latex2e, no figures

C∗-extensions of tori, higher Chow groups and applications to incidence equivalence relations for algebraic cycles.

Abstract

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