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

2013/06/11 by Eisentraeger, Kirsten, Shlapentokh, Alexandra · 1 citation
#03C07 #03D35 #11U05 #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1306.2669

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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• Decidability of polynomial equations over function fields in positive characteristic

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