Axiomatizing the existential theory of Fq((t))
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
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.
Details
Original language | English |
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Pages (from-to) | 2013-2032 |
Number of pages | 20 |
Journal | Algebra & number theory |
Volume | 17 |
Issue number | 11 |
Publication status | Published - 3 Oct 2023 |
Peer-reviewed | Yes |
External IDs
Scopus | 85174322585 |
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Mendeley | 0c80bea6-0a26-3f45-b04b-b1df7fd23271 |
Keywords
ASJC Scopus subject areas
Keywords
- decision algorithm, existential theory, henselian valued field, local fields, local uniformization, positive characteristic, resolution of singularities