Space of one cycles and coniveau filtrations
Algebraic Geometry
2023-02-20 v2
Abstract
We prove a structural result about the space of one cycles of a separably rationally connected variety or a separably rationally connected fibration over a curve, either as a topological group or as an h-sheaf. This has the following consequences: a proof that the strong coniveau filtration agrees with the coniveau filtration on degree 3 homology, and a result on the integral Tate conjecture for homologically trivial one cycles.
Keywords
Cite
@article{arxiv.2211.15911,
title = {Space of one cycles and coniveau filtrations},
author = {Zhiyu Tian},
journal= {arXiv preprint arXiv:2211.15911},
year = {2023}
}
Comments
The part of deformations of stable maps and algebraic equivalence is replaced by a joint paper with J\'anos Koll\'ar as arXiv:2302.07069, with stronger results and simplified proof. The part about coniveau filtrations and applications to cycle class maps will be included in the revised version of arXiv:2211.15915