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This article is cited in 2 scientific papers (total in 2 papers)
Research Papers
Some remarks on Leopoldt's conjecture
F. Lorenz
Abstract:
Let $k$ be a number field, and let $p$ be a fixed prime number. Then the
vanishing of the Leopoldt kernel $\mathscr{L}_p(k)$ is shown to be equivalent to the validity of
a "Strong Local-Global Principle on units of $k$". This adds a problem of effectivity
to Leopoldt's conjecture (an example to which is provided by the classical Kummer
lemma on the $p$th powers of units in the field of the $p$th roots of unity). Some further
remarks pertain to $\mathscr{L}_p(k)$ as a Galois module. For example, if $k/{\mathbb Q}$ is an Abelian $p$-extension,
then the triviality of $\mathscr{L}_p(k)$ can be shown quite easily (in particular, without
using Brumer's transcendency theorem).
Received: 26.04.1998
Citation:
F. Lorenz, “Some remarks on Leopoldt's conjecture”, Algebra i Analiz, 10:6 (1998), 144–155; St. Petersburg Math. J., 10:6 (1999), 1005–1013
Linking options:
https://www.mathnet.ru/eng/aa1036 https://www.mathnet.ru/eng/aa/v10/i6/p144
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