Restricted trichotomy in characteristic zero

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2023-10-03 DOI:10.1090/jams/1037

Benjamin Castle

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引用次数: 0

Abstract

We prove the characteristic zero case of Zilber’s Restricted Trichotomy Conjecture. That is, we show that if M \mathcal M is any non-locally modular strongly minimal structure interpreted in an algebraically closed field K K of characteristic zero, then M \mathcal M itself interprets K K ; in particular, any non-1-based structure interpreted in K K is mutually interpretable with K K . Notably, we treat both the ‘one-dimensional’ and ‘higher-dimensional’ cases of the conjecture, introducing new tools to resolve the higher-dimensional case and then using the same tools to recover the previously known one-dimensional case.

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特征零点受限三分法

证明了Zilber有限三分猜想的特征零情况。即，我们证明如果M \mathcal M是在特征为0的代数闭域K K中解释的任何非局部模强极小结构，则M \mathcal M本身解释K K;特别地，任何用K K解释的非1基结构都是与K K相互解释的。值得注意的是，我们同时处理了该猜想的“一维”和“高维”情况，引入了新的工具来解决高维情况，然后使用相同的工具来恢复先前已知的一维情况。

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

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.