Applications of Baker Theory to the Conjecture of Leopoldt

Details Applications of Baker Theory to the Conjecture of Leopoldt Applications of Baker Theory to the Conjecture of Leopoldt

2009-09-15

arxiv.org/abs/0909.2738v2

Mathematics

Number Theory

We prove the two extreme cases of the Leopoldt conjecture in which K/Q is a real galois extension which either has a solvable

Scientific paper

In this paper we give a short, elementary proof of the following too extreme cases of the Leopoldt conjecture: the case when $\K/\Q$ is a solvable extension and the case when it is a totally real extension in which $p$ splits completely. The first proof uses Baker theory, the second class field theory. The methods used here are a sharpening of the ones presented at the SANT meeting in G\"ottingen, 2008 and exposed in \cite{Mi2}, \cite{Mi1}.

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