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Inductive construction of the $p$-adic zeta functions for non-commutative $p$-extensions of totally real fields with exponent $p$.

Втр, 08/18/2009 - 11:53 — SomNambul
Authors: Takashi Hara
Subjects: Number Theory
link: http://arxiv.org/abs/0908.2178
Abstract

In this paper, we will construct the p-adic zeta function for a
non-commutative p-extension of a totally real number field such that the finite
part of its Galois group is a p-group with exponent p. We first calculate the
Whitehead groups of the Iwasawa algebra and its canonical Ore localization by
using Oliver-Taylor's theory on integral logarithms. Then we reduce the main
conjecture to certain congruences among abelian p-adic zeta pseudomeasures
constructed by Deligne-Ribet and Serre. Finally we prove these congruences by
using the theory of Deligne-Ribet and certain induction. The main results of
this paper give generalization of those of the preceding paper.

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