Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields

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Abstract

Let k be a subfield of a p-adic field of odd residue characteristic, and let L be the function field of a variety of dimension n ≥ 1 over k. Then Hilbert's Tenth Problem for L is undecidable. In particular, Hilbert's Tenth Problem for function fields of varieties over number fields of dimension ≥1 is undecidable.

Original languageEnglish (US)
Pages (from-to)775-792
Number of pages18
JournalJournal of Algebra
Volume310
Issue number2
DOIs
StatePublished - Apr 15 2007

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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