Higher l-adic Abel-Jacobi mappings and filtrations on Chow groups

1994/12/02 by Wayne M. Raskind, Raskind, Wayne M.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9412001

33 pages, Latex. To appear in Duke Math. Journal

arxiv created 1994/12/02 · arxiv updated 2009/11/30

Abstract

We define a filtration on the Chow groups of a smooth projective variety X over a field k by using the cycle map into continuous l-adic etale cohomology. The main theorem says that if k is a function field in one variable over a finite field, this filtration for zero cycles is of length at most one modulo the kernel of the cycle map.

Related

• A filtration on the higher Chow group of zero cycles on an abelian variety
• Filtrations on the Chow groups and transcendence degree
• The Abel-Jacobi map for higher Chow groups
• Filtrations of the Chow group of zero-cycles on abelian varieties and behavior under isogeny
• The Étale Homology and The Cycle Maps in Adic Coefficients