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PreprintCC BY 4.0arXiv

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

  • Antoine Ducros
  • François Loeser
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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.

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Cite

BibTeXRIS
BibTeX
@misc{ducros2026nash,
  title = {{Nash structure of curves over a valued field and tame henselian rationality}},
  author = {Antoine Ducros and François Loeser},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.00659},
  eprint = {2608.00659},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.00659},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Nash structure of curves over a valued field and tame henselian rationality
AU  - Antoine Ducros
AU  - François Loeser
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2608.00659
UR  - https://arxiv.org/abs/2608.00659
AB  - 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.
ER  -