Adelic Euler systems for $\GG_m$

TY - JOUR

T1 - Adelic Euler systems for $\GG_m$

AU - Daoud, Alexandre

AU - Burns, David

PY - 2022/1/11

Y1 - 2022/1/11

N2 - We define a notion of adelic Euler systems for $\GG_m$ over arbitrary number fields and prove that all such systems over $\QQ$ are cyclotomic in nature. We deduce that all Euler systems for $\mathbb{G}_m$ over $\QQ$ are cyclotomic, as has been conjectured by Coleman, if and only if they validate an analogue of Leopoldt's Conjecture. We show that the latter prediction entails consequences for the structure of Selmer modules.

AB - We define a notion of adelic Euler systems for $\GG_m$ over arbitrary number fields and prove that all such systems over $\QQ$ are cyclotomic in nature. We deduce that all Euler systems for $\mathbb{G}_m$ over $\QQ$ are cyclotomic, as has been conjectured by Coleman, if and only if they validate an analogue of Leopoldt's Conjecture. We show that the latter prediction entails consequences for the structure of Selmer modules.

KW - Euler systems

KW - Iwasawa Theory

M3 - Article

SN - 0040-8735

JO - TOHOKU MATHEMATICAL JOURNAL

JF - TOHOKU MATHEMATICAL JOURNAL

ER -