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Intersection of valuation rings in k[x, y]

Junyi Xie IRMAR, CNRS

Arithmetic Geometry and Commutative Algebra mathscidoc:1908.07001

Proc. London Math. Soc. , 2015
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.
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@inproceedings{junyi2015intersection,
  title={Intersection of valuation rings in k[x, y]},
  author={Junyi Xie},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190821182052417518433},
  booktitle={Proc. London Math. Soc. },
  year={2015},
}
Junyi Xie. Intersection of valuation rings in k[x, y]. 2015. In Proc. London Math. Soc. . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190821182052417518433.
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