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Prime decomposition and the Iwasawa MU-invariant

Published online by Cambridge University Press:  26 April 2018

FARSHID HAJIR  and
CHRISTIAN MAIRE
FARSHID HAJIR
Affiliation:
Department of Mathematics & Statistics, University of Massachusetts, Amherst MA 01003, U.S.A. e-mail: hajir@math.umass.edu
CHRISTIAN MAIRE
Affiliation:
Laboratoire de Mathématiques de Besançon, Université Bourgogne Franche-Comté et CNRS, 16 route de Gray, 25030 Besançon, France. e-mail: christian.maire@univ-fcomte.fr
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Abstract

For Γ = ℤp, Iwasawa was the first to construct Γ-extensions over number fields with arbitrarily large μ-invariants. In this work, we investigate other uniform pro-p groups which are realisable as Galois groups of towers of number fields with arbitrarily large μ-invariant. For instance, we prove that this is the case if p is a regular prime and Γ is a uniform pro-p group admitting a fixed-point-free automorphism of odd order dividing p−1. Both in Iwasawa's work, and in the present one, the size of the μ-invariant appears to be intimately related to the existence of primes that split completely in the tower.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 3 , May 2019 , pp. 599 - 617
Copyright
Copyright © Cambridge Philosophical Society 2018 

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