Hilbert's Tenth Problem for rational function fields over p-adic fields

JOURNAL OF ALGEBRA

卷:361

Article

Degroote, Claudia¹  Demeyer, Jeroen¹ 

[1] Univ Ghent, Dept Math, B-9000 Ghent, Belgium

关键词: Undecidability;    Valuations;    Quadratic forms;   

DOI  :  10.1016/j.jalgebra.2012.03.039

来源: Elsevier

【 摘 要 】

Let K be a p-adic field (a finite extension of some Q(p)) and let K(t) be the field of rational functions over K. We define a kind of quadratic reciprocity symbol for polynomials over K and apply it to prove isotropy for a certain class of quadratic forms over K(t). Using this result, we give an existential definition for the predicate v(t)(x) >= 0 in K (t). This implies undecidability of diophantine equations over K(t). (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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