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arxiv: 1303.0176 · v1 · pith:RO4KPN3Jnew · submitted 2013-03-01 · 🧮 math.NT

On universal norms and the first layers of Z_p-extensions of a number field

classification 🧮 math.NT
keywords fieldfirstlayersnormsnumberp-extensionsuniversalalong
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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 A_F of the first layers of all the 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 AF .

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