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Cylindrical homomorphisms and Lawson homology

Published online by Cambridge University Press:  08 June 2010

Mircea Voineagu
Mircea Voineagu
Affiliation:
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA, voineagu@usc.edu
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Abstract

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

Keywords

Lawson homologymotivic cohomologysemi-topological K-theory
Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 1 , August 2011 , pp. 135 - 168
Copyright
Copyright © ISOPP 2010

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