Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field

Kirsten Eisenträger, Alexandra Shlapentokh

Research output: Contribution to journalArticle

Abstract

We prove that the existential theory of any function field K of characteristic p > 0 is undecidable in the language of rings augmented by constant symbols for the elements of a suitable recursive subfield, provided that the constant field does not contain the algebraic closure of a finite field. This theorem is the natural generalization of a theorem of Kim and Roush from 1992. We also extend our previous undecidability proof for function fields of higher transcendence degree to characteristic 2 and show that the first-order theory of any function field of positive characteristic is undecidable in the language of rings without parameters.

Original languageEnglish (US)
Pages (from-to)2103-2138
Number of pages36
JournalJournal of the European Mathematical Society
Volume19
Issue number7
DOIs
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Hilbert's Tenth Problem over function fields of positive characteristic not containing the algebraic closure of a finite field'. Together they form a unique fingerprint.

  • Cite this