Number fields generated by points in linear systems on curves

Irmak Balçik; Stephanie Chan; Yuan Liu; Bianca Viray

Number fields generated by points in linear systems on curves

Number Theory 2025-09-23 v2 Algebraic Geometry

Authors: Irmak Balçik , Stephanie Chan , Yuan Liu , Bianca Viray

Abstract

We develop techniques for determining the fibers of a morphism of curves $\phi: C \to D$ over a nonarchimedean local field $K$ . These results have applications to studying closed point on curves over global fields since closed points on $C$ of large degree or of very small degree are known to all arise as fibers of morphisms.

Keywords

curves fibrations algebraic curves

Cite

@article{arxiv.2503.07846,
  title  = {Number fields generated by points in linear systems on curves},
  author = {Irmak Balçik and Stephanie Chan and Yuan Liu and Bianca Viray},
  journal= {arXiv preprint arXiv:2503.07846},
  year   = {2025}
}

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24 pages

Number fields generated by points in linear systems on curves

Abstract

Keywords

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