Algebra & Number Theory

The existential theory of equicharacteristic henselian valued fields

Sylvy Anscombe and Arno Fehm

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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)).

Article information

Source
Algebra Number Theory, Volume 10, Number 3 (2016), 665-683.

Dates
Received: 18 September 2015
Revised: 9 February 2016
Accepted: 15 March 2016
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842499

Digital Object Identifier
doi:10.2140/ant.2016.10.665

Mathematical Reviews number (MathSciNet)
MR3513134

Zentralblatt MATH identifier
1377.03025

Subjects
Primary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
Secondary: 12L12: Model theory [See also 03C60] 12J10: Valued fields 11U05: Decidability [See also 03B25] 12L05: Decidability [See also 03B25]

Keywords
model theory henselian valued fields decidability diophantine equations

Citation

Anscombe, Sylvy; Fehm, Arno. The existential theory of equicharacteristic henselian valued fields. Algebra Number Theory 10 (2016), no. 3, 665--683. doi:10.2140/ant.2016.10.665. https://projecteuclid.org/euclid.ant/1510842499


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