Intersection of valuation rings in $k[x,y]$
Algebraic Geometry
2015-06-12 v1
Abstract
We associate to any given finite set of valuations on the polynomial ring in two variables over an algebraically closed field a numerical invariant whose positivity characterizes the case when the intersection of their valuation rings has maximal transcendence degree over the base fields. As an application, we give a criterion for when an analytic branch at infinity in the affine plane that is defined over a number field in a suitable sense is the branch of an algebraic curve.
Keywords
Cite
@article{arxiv.1403.6052,
title = {Intersection of valuation rings in $k[x,y]$},
author = {Junyi Xie},
journal= {arXiv preprint arXiv:1403.6052},
year = {2015}
}