$\mathbb{G}_m$的阿德利克欧拉系统

IF 0.4 4区数学 Q4 MATHEMATICS

Tohoku Mathematical Journal Pub Date : 2023-09-01 DOI:10.2748/tmj.20220111

David Burns, Alexandre Daoud

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引用次数: 0

摘要

我们定义了任意数域上$\mathbb{G}_m$的阿得利克欧拉系统的概念，并证明了$\mathbb{Q}$上的所有阿得利克欧拉系统本质上都是环切分的。我们推导出，对于$\mathbb{G}_m$ / $\mathbb{Q}$的所有欧拉系统，当且仅当它们验证了利奥波德猜想的类似物，如Coleman所推测的那样，都是环切分的。

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Adelic Euler systems for $\mathbb{G}_m$

We define a notion of adelic Euler systems for $\mathbb{G}_m$ over arbitrary number fields and prove that all such systems over $\mathbb{Q}$ are cyclotomic in nature. We deduce that all Euler systems for $\mathbb{G}_m$ over $\mathbb{Q}$ are cyclotomic, as has been conjectured by Coleman, if and only if they validate an analogue of Leopoldt's Conjecture.

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