%0 Journal Article
%T Leopoldt's Conjecture for CM fields
%A Preda Mihailescu
%J Mathematics
%D 2011
%I arXiv
%X The conjecture of Leopoldt states that the $p$ - adic regulator of a number field does not vanish. It was proved for the abelian case in 1967 by Brumer, using Baker theory. We prove this conjecture for CM number fields $\K$. The proof uses Iwasawa's methods -- especially Takagi Theory -- for deriving his skew symmetric pairing, together with Kummer- and Class Field Theory.
%U http://arxiv.org/abs/1105.4544v3