Year: 2013
Author: Ting Li
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 68–87
Abstract
In this article, we define the $ℓ$-adic homology for a morphism of schemes satisfying certain finiteness conditions. This homology has these functors similar to the Chow groups: proper push-forward, flat pull-back, base change, cap-product, etc. In particular, on singular varieties, this kind of $ℓ$-adic homology behaves much better than the classical $ℓ$-adic cohomology. As an application, we give a much easier approach to construct the cycle maps for arbitrary algebraic schemes over fields. And we prove that these cycle maps kill the algebraic equivalences and commute with the Chern action of locally free sheaves.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-CMR-19030
Communications in Mathematical Research , Vol. 29 (2013), Iss. 1 : pp. 68–87
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: $ℓ$-adic cohomology cycle map derived category.