Tohoku Mathematical Journal
2023
September
SECOND SERIES VOL. 75, NO. 3

Tohoku Math. J.
75 (2023), 329-346

Title ADELIC EULER SYSTEMS FOR $\mathbb{G}_m$

Author David Burns and Alexandre Daoud

(Received May 20, 2020, revised January 11, 2022)
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.

Mathematics Subject Classification. Primary 11R42; Secondary 11R27.
Key words and phrases. Euler systems, Iwasawa Theory.

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