Download this article
 Download this article For screen
For printing
Recent Issues

Volume 18
Issue 7, 1221–1401
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
Editors' interests
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author index
To appear
Other MSP journals
Axiomatizing the existential theory of $\mathbb{F}_q((t))$

Sylvy Anscombe, Philip Dittmann and Arno Fehm

Vol. 17 (2023), No. 11, 2013–2032

We study the existential theory of equicharacteristic henselian valued fields with a distinguished uniformizer. In particular, assuming a weak consequence of resolution of singularities, we obtain an axiomatization of — and therefore an algorithm to decide — the existential theory relative to the existential theory of the residue field. This is both more general and works under weaker resolution hypotheses than the algorithm of Denef and Schoutens, which we also discuss in detail. In fact, the consequence of resolution of singularities our results are conditional on is the weakest under which they hold true.

local fields, positive characteristic, henselian valued field, existential theory, decision algorithm, resolution of singularities, local uniformization
Mathematical Subject Classification
Primary: 03C60, 11D88, 11G25, 12L05
Received: 2 June 2022
Revised: 15 January 2023
Accepted: 6 March 2023
Published: 3 October 2023
Sylvy Anscombe
Institut de Mathématiques de Jussieu-Paris Rive Gauche
Université Paris Cité
Philip Dittmann
Institut fĂĽr Algebra
Technische Universität Dresden
Arno Fehm
Institut fĂĽr Algebra
Technische Universität Dresden

Open Access made possible by participating institutions via Subscribe to Open.