2006•arXiv (Cornell University)Open access

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

Kirsten Eisentraeger

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.

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Key concepts: Undecidable problem, Mathematics, Dimension (graph theory), Function field, Pure mathematics, Function (biology), Field (mathematics), Variety (cybernetics)