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arXiv · 1105.4544

Leopoldt's Conjecture for CM fields

Preda Mihailescu
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Abstract

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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Preda Mihailescu. 2011-05-23. Leopoldt's Conjecture for CM fields. https://arxiv.org/abs/1105.4544

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