Type-definable NIP fields are Artin-Schreier closed

Will Johnson

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arXiv · 2201.02778

Type-definable NIP fields are Artin-Schreier closed

Will Johnson

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Abstract

Let $K$ be a type-definable infinite field in an NIP theory. If $K$ has characteristic $p > 0$, then $K$ is Artin-Schreier closed (it has no Artin-Schreier extensions). As a consequence, $p$ does not divide the degree of any finite separable extension of $K$. This generalizes a theorem of Kaplan, Scanlon, and Wagner.

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BibTeX RIS

Will Johnson. 2022-01-08. Type-definable NIP fields are Artin-Schreier closed. https://arxiv.org/abs/2201.02778

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