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arXiv · 2604.26129

Elimination results for tame fields with finite residue fields

Sylvy Anscombe·Blaise Boissonneau
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Abstract

Building on work of Kuhlmann and Lisinski, we study the theory of the Hahn series field $\mathbb{F}_{q}(\!(\mathbb{Q})\!)$, over a finite field $\mathbb{F}_{q}$, equipped with the $t$-adic valuation, in a language of valued fields. We prove that every formula is equivalent to a formula $\exists y\colon f(x_{1},\ldots,x_{n},y)=0$, for a polynomial $f\in\mathbb{Z}[x_{1},\ldots,x_{n},y]$.

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BibTeXRIS

Sylvy Anscombe, Blaise Boissonneau. 2026-04-28. Elimination results for tame fields with finite residue fields. https://arxiv.org/abs/2604.26129

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