Axiomatizing the existential theory of 𝔽q((t))

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2023-10-03 DOI:10.2140/ant.2023.17.2013

Sylvy Anscombe, Philip Dittmann, Arno Fehm

引用次数: 2

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.

查看原文本刊更多论文

我们研究了等特征henselian值域的存在论与一个可分辨的一致化子。特别是，假设奇点的解析结果很弱，我们得到了存在论相对于剩余域的存在论的公理化，从而得到了决定存在论的算法。这比我们也详细讨论的Denef和Schoutens的算法更通用，并且在较弱的分辨率假设下工作。事实上，我们的结果所依赖的奇点的解析结果是它们成立的最弱条件。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： ANT’s inclusive definition of algebra and number theory allows it to print research covering a wide range of subtopics, including algebraic and arithmetic geometry. ANT publishes high-quality articles of interest to a broad readership, at a level surpassing all but the top four or five mathematics journals. It exists in both print and electronic forms. The policies of ANT are set by the editorial board — a group of working mathematicians — rather than by a profit-oriented company, so they will remain friendly to mathematicians'' interests. In particular, they will promote broad dissemination, easy electronic access, and permissive use of content to the greatest extent compatible with survival of the journal. All electronic content becomes free and open access 5 years after publication.