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

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

2006-10-04

arxiv.org/abs/math/0610132v1

Mathematics

Number Theory

19 pages; to appear in Journal of Algebra

Scientific paper

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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