Hilbert's Tenth Problem for function fields of varieties over algebraically closed fields of positive characteristic

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Abstract

Let K be the function field of a variety of dimension ≥ 2 over an algebraically closed field of odd characteristic. Then Hilbert's Tenth Problem for K is undecidable. This generalizes the result by Kim and Roush from 1992 that Hilbert's Tenth Problem for the purely transcendental function field F p(t 1, t 2) is undecidable when p > 2.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalMonatshefte fur Mathematik
Volume168
Issue number1
DOIs
StatePublished - Oct 1 2012

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Hilbert's Tenth Problem
Positive Characteristic
Function Fields
Algebraically closed
Transcendental function
Odd
Generalise

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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abstract = "Let K be the function field of a variety of dimension ≥ 2 over an algebraically closed field of odd characteristic. Then Hilbert's Tenth Problem for K is undecidable. This generalizes the result by Kim and Roush from 1992 that Hilbert's Tenth Problem for the purely transcendental function field F p(t 1, t 2) is undecidable when p > 2.",
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