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ADELIC EULER SYSTEMS FOR GM

David Burns,Alexandre Daoud

TOHOKU MATHEMATICAL JOURNAL（2023）

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Abstract
We define a notion of adelic Euler systems for G(m )over arbitrary number fields and prove that all such systems over Q are cyclotomic in nature. We deduce that all Euler systems for G(m )over 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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Key words
Euler systems, Iwasawa Theory
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