Beilinson's Hodge conjecture for smooth varieties
Algebraic Geometry
2011-04-25 v1
Abstract
Consider the cycle class map cl_{r,m} : CH^r(U,m;\Q) \to \Gamma H^{2r-m}(U,\Q(r)), where CH^r(U,m;\Q) is Bloch's higher Chow group (tensored with \Q) of a smooth complex quasi-projective variety U, and H^{2r-m}(U,\Q(r)) is singular cohomology. We study the image of cl_{r,m} in terms of kernels of Abel-Jacobi maps. When r=m, we deduce from the Bloch-Kato theorem that the cokernel of cl_{r,m} at the generic point of U is the same for integral or rational coefficients.
Cite
@article{arxiv.1104.4364,
title = {Beilinson's Hodge conjecture for smooth varieties},
author = {Rob de Jeu and James D. Lewis},
journal= {arXiv preprint arXiv:1104.4364},
year = {2011}
}
Comments
33 pages