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

Abstract

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.