A comparison between obstructions to local-global principles over semiglobal fields
Number Theory
2020-06-15 v3 Algebraic Geometry
Abstract
We consider local-global principles for rational points on varieties, in particular torsors, over one-variable function fields over complete discretely valued fields. There are several notions of such principles, arising either from the valuation theory of the function field, or from the geometry of a regular model of the function field. Our results compare the corresponding obstructions, proving in particular that a local-global principle with respect to valuations implies a local-global principle with respect to a sufficiently fine regular model.
Cite
@article{arxiv.1903.08007,
title = {A comparison between obstructions to local-global principles over semiglobal fields},
author = {David Harbater and Julia Hartmann and Valentijn Karemaker and Florian Pop},
journal= {arXiv preprint arXiv:1903.08007},
year = {2020}
}
Comments
10 pages; published version