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

2006/10/04 by Kirsten Eisentraeger, Eisentraeger, Kirsten · 1 citation
Computer Science · Mathematics · #03B25 (Secondary) #11U05 (Primary) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0610132

openalex publication_date 2006/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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