Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields
Abstract
We study the existence of zero-cycles of degree one on varieties that are defined over a function field of a curve over a complete discretely valued field. In particular, we show that local-global principles hold for such zero-cycles provided that local-global principles hold for the existence of rational points over extensions of the function field. This assertion is analogous to a known result concerning varieties over number fields. We also show that our results hold more generally in the henselian case.
Keywords
Cite
@article{arxiv.1710.03173,
title = {Local-Global Principles for Zero-Cycles on Homogeneous Spaces over Arithmetic Function Fields},
author = {Jean-Louis Colliot-Thélène and David Harbater and Julia Hartmann and Daniel Krashen and R. Parimala and V. Suresh},
journal= {arXiv preprint arXiv:1710.03173},
year = {2018}
}
Comments
23 pages. Some explanations were expanded for greater clarity throughout the paper. Some results in Section 2 in the earlier version in the complete case were generalized here to the henselian case. Subsection 3.3 in the earlier version was broken into two subsections, and there was some renumbering of results in the new Subsection 3.4 due to an added remark