Nash structure of curves over a valued field and tame henselian rationality

Antoine Ducros; François Loeser

Nash structure of curves over a valued field and tame henselian rationality

Algebraic Geometry 2026-08-01 v1 Commutative Algebra Logic

Authors: Antoine Ducros , François Loeser

Abstract

We provide a new proof, model-theoretic and geometric in nature, of the tame henselian rationality theorem of Kuhlmann. The proof takes place within the framework of stable completions of algebraic varieties over a valued field. It relies on the proof of two main results of independent interest: a Nash structure theorem for the stable completion of an algebraic curve and a tame descent theorem for abstract polydiscs.

Keywords

tame henselian rationality stable completions Nash structure algebraic curves valued fields model theory

Cite

@article{arxiv.2608.00659,
  title  = {Nash structure of curves over a valued field and tame henselian rationality},
  author = {Antoine Ducros and François Loeser},
  journal= {arXiv preprint arXiv:2608.00659},
  year   = {2026}
}

Comments

74 pages