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

Kirsten Eisentraeger

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arXiv · math/0610132

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

Kirsten Eisentraeger

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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.

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Kirsten Eisentraeger. 2006-10-04. Hilbert's Tenth Problem for function fields of varieties over number fields and p-adic fields. https://arxiv.org/abs/math/0610132

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