Leopoldt's Conjecture for CM fields

Details Leopoldt's Conjecture for CM fields Leopoldt's Conjecture for CM fields

2011-05-23

arxiv.org/abs/1105.4544v2

Mathematics

Number Theory

I decided to rewrite the material in the T and T^* parts and SNOQIT in smaller, detailed chunks. This is the first, containing

Scientific paper

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.

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