Characterizing finitely generated fields by a single field axiom

• 成果类型: Article
• 署名作者: Dittmann, Philip; Pop, Florian
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.198.3.4
• 发表日期: 2023
• 页码: 1203-1227
• 关键词: elementary equivalence; K-THEORY; Isomorphism; forms

摘要

We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class, there is a first-order sentence that 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.