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

Anne Kirsten Eisentraeger

doi:10.1007/s00605-011-0364-7

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

Anne Kirsten Eisentraeger

Mathematics

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4 Scopus citations

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 language	English (US)
Pages (from-to)	1-16
Number of pages	16
Journal	Monatshefte fur Mathematik
Volume	168
Issue number	1
DOIs	https://doi.org/10.1007/s00605-011-0364-7
State	Published - Oct 1 2012

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00605-011-0364-7

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

Abstract

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