One-dimensional F-definable sets in F((t))
| Autor: | Anscombe, Will |
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| Rok vydání: | 2015 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1503.05803 |
| Popis: | We study definable sets in power series fields with perfect residue fields. We show that certain `one-dimensional' definable sets are in fact existentially definable. This allows us to apply results from previous work about existentially definable sets to one-dimensional definable sets. More precisely, let $F$ be a perfect field and let a be a tuple from $F((t))$ of transcendence degree 1 over $F$. Using the description of $F$-automorphisms of $F((t))$ given by Schilling, we show that the orbit of a under $F$-automorphisms is existentially definable in the ring language with parameters from $F(t)$. We deduce the following corollary. Let $X$ be an $F$-definable subset of $F((t))$ which is not contained in $F$, then the subfield generated by $X$ is equal to $F((t^{p^n}))$, for some $n Comment: 11 pages |
| Databáze: | OpenAIRE |
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