The Étale Homology and the Cycle Maps in Adic Coefficients

The Étale Homology and the Cycle Maps in Adic Coefficients

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.

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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.

Author Details

Ting Li