The existential theory of equicharacteristic henselian valued fields

Anscombe, Sylvy orcid iconORCID: 0000-0002-9930-2804 and Fehm, Arno (2016) The existential theory of equicharacteristic henselian valued fields. Algebra and Number Theory, 10 (3). pp. 665-683. ISSN 1937-0652

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Official URL: http://doi.org/10.2140/ant.2016.10.665

Abstract

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 Fq((t)).


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