Characterizing finitely generated fields by a single field axiom

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2023-11-01 DOI:10.4007/annals.2023.198.3.4

Philip Dittmann, Florian Pop

引用次数: 1

Abstract

We resolve the Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is an explicit first-order sentence which characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.

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用单域公理描述有限生成域

我们解决了有限生成域的初等等价与同构问题。也就是说，我们证明，对于类中的每个字段，都有一个明确的一阶句子来表征类中的这个字段直至同构。我们的解以特征二的奇点的解为条件，而其他所有特征的解都是无条件的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.