Applications of Baker Theory to the Conjecture of Leopoldt

2009/09/15 by Preda Mihăilescu, Mihăilescu, Preda
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #math.NT #msc:11R23 #msc:11R27

paper · pdf · doi:10.48550/arxiv.0909.2738

Outdated approach to Leopoldt, replaced by Version from March 2014

arxiv created 2015/02/17 · arxiv updated 2015/02/18

Abstract

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 Göttingen, 2008 and exposed in \citeMi2, \citeMi1.

Related

• Leopoldt's Conjecture for CM fields
• Applications of representation theory and of explicit units to Leopoldt's conjecture
• Exchanging the places p and infinity in the Leopoldt conjecture
• A Variation on Leopoldt's Conjecture: Some Local Units instead of All Local Units
• The Leopoldt and Iwasawa Conjectures for CM fields