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On universal norms and the first layers of \(\mathbb {Z}_p\)-extensions of a number field

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For an odd prime \(p\) and a number field \(F\) containing a primitive \(p\)-th root of unity, we describe the Kummer radical \({\mathcal {A}}_F\) of the first layers of all the \(\mathbb {Z}_p\)-extensions of \(F\) in terms of universal norms of \(p\)-units along the cyclotomic tower of \(F\). We also study “twisted” radicals related to \({\mathcal {A}}_F\).

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Movahhedi, A., Nguyen Quang Do, T. On universal norms and the first layers of \(\mathbb {Z}_p\)-extensions of a number field. Math. Ann. 362, 817–838 (2015). https://doi.org/10.1007/s00208-014-1134-3

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  • DOI: https://doi.org/10.1007/s00208-014-1134-3

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