The existential theory of equicharacteristic henselian valued fields

被引:10
作者
Anscombe, Sylvy [1 ]
Fehm, Arno [2 ]
机构
[1] Univ Cent Lancashire, Jeremiah Horrocks Inst, Preston PR1 2HE, Lancs, England
[2] Univ Manchester, Sch Math, Oxford Rd, Manchester M13 9PL, Lancs, England
基金
英国工程与自然科学研究理事会;
关键词
model theory; henselian valued fields; decidability; diophantine equations; FINITE;
D O I
10.2140/ant.2016.10.665
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the existential (and parts of the universal-existential) theory of equicharacteristic henselian valued fields. We prove, among other things, an existential Ax-Kochen-Ershov principle, which roughly says that the existential theory of an equicharacteristic henselian valued field (of arbitrary characteristic) is determined by the existential theory of the residue field; in particular, it is independent of the value group. As an immediate corollary, we get an unconditional proof of the decidability of the existential theory of F-q((t)).
引用
收藏
页码:665 / 683
页数:19
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