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arXiv · 1306.2669

Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field

Kirsten Eisentraeger·Alexandra Shlapentokh
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Abstract

We prove that the existential theory of any function field $K$ of characteristic $p> 0$ is undecidable in the language of rings provided that the constant field does not contain the algebraic closure of a finite field. We also extend the undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of {\bf any} function field of positive characteristic is undecidable in the language of rings without parameters.

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Kirsten Eisentraeger, Alexandra Shlapentokh. 2013-06-11. Hilbert's Tenth Problem over Function Fields of Positive Characteristic Not Containing the Algebraic Closure of a Finite Field. https://arxiv.org/abs/1306.2669

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