Cylindrical Homomorphisms and Lawson Homology

Details Cylindrical Homomorphisms and Lawson Homology Cylindrical Homomorphisms and Lawson Homology

2009-04-22

arxiv.org/abs/0904.3374v1

Mathematics

Algebraic Geometry

to appear in Journal of K-theory

Scientific paper

We use the cylindrical homomorphism and a geometric construction introduced by J. Lewis to study the Lawson homology groups of certain hypersurfaces $X\subset \mathbb{P}^{n+1}$ of degree $d\leq n+1$. As an application, we compute the rational semi-topological K-theory of a generic cubic of dimension 5, 6 and 8 and, using the Bloch-Kato conjecture, we prove Suslin's conjecture for these varieties. Using the generic cubic sevenfolds, we show that there are smooth projective varieties with the lowest non-trivial step in their s-filtration infinitely generated and undetected by the Abel-Jacobi map.

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