Journal
ALGEBRA & NUMBER THEORY
Volume 10, Issue 3, Pages 665-683Publisher
MATHEMATICAL SCIENCE PUBL
DOI: 10.2140/ant.2016.10.665
Keywords
model theory; henselian valued fields; decidability; diophantine equations
Categories
Funding
- EPSRC [EP/K020692/1]
- Engineering and Physical Sciences Research Council [EP/K020692/1] Funding Source: researchfish
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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)).
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