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Hasse-Arf Property and Abelian Extensions

✍ Scribed by Ivan B. Fesenko

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
323 KB
Volume
174
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The paper contains discussions of relations between the property of a totally ramified p‐extension of a local field to be abelian and the property of its Galois group to possess integer jumps with respect to the upper numbering (Hasse‐Arf property). It is shown that such an extension L/F is abelian if and only if for any totally ramified abelian extension E/F the extension LE/F satisfies the Hasse‐Arf property. An additional property to the Hasse‐Arf property in terms of principal units which makes the extension abelian is established as well.

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It is a pleasure to thank the referec for his valuable suggestions which resulted in an improvement of the manuscript. The first author also thanks Professor E. L. Green for valuable discussions concerning the package GRB, on May 1994 at SFB 343, University Bielefeld; and Professor C. M. Ringel for