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Pré-Publication, Document De Travail Année : 2017

The p-adic Kummer-Leopoldt constant -- Normalized p-adic regulator

Résumé

The p-adic Kummer--Leopoldt constant kappa(K) of a number field K is (under the Leopoldt conjecture for p in K) the least integer c such that for all n large enough, any global unit epsilon of K, which is locally (at the p-places) a p^{n+c}th power, is necessarily a p^{n}th power of a global unit of K. This constant has been computed by J. Assim and T. Nguyen Quang Do using Iwasawa's technics. In this short Note, we give an elementary p-adic proof of their result and the class field theory interpretation of kappa(K) by means of Abelian p-ramification theory over K. Then, from this, we give a natural definition of the normalized p-adic regulator of K, for any K and any p≥2.
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Dates et versions

hal-01444560 , version 1 (24-01-2017)
hal-01444560 , version 2 (31-03-2017)

Identifiants

Citer

Georges Gras. The p-adic Kummer-Leopoldt constant -- Normalized p-adic regulator. 2017. ⟨hal-01444560v1⟩
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