Ramification Groups of Nonabelian Kummer Extensions

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The reciprocity law of Coleman for the Hilbert norm residue symbol has allowed the computation of the conductors of the abelian Kummer extensionsQp(a,ζpn)/Qppn)witha∈Qpandζpna primitive (pn)th root of unity for a fixed primepand all positive integersn. From these conductors, we compute the ramification groups of the nonabelian Kummer extensionQp(Q×p)/Qpobtained from adjoining toQpallp-power roots of its elements. More generally, given a similar nonabelian Kummer extension of complete discrete valuation fields, we have a method of computing its ramification groups from the conductors of the abelian Kummer extensions and knowledge of the ramification groups of the cyclotomic extensions.

Original languageEnglish (US)
Pages (from-to)105-115
Number of pages11
JournalJournal of Number Theory
Volume65
Issue number1
DOIs
StatePublished - Jul 1997
Externally publishedYes

Fingerprint

Ramification
Conductor
Reciprocity Law
Cyclotomic
Roots of Unity
Valuation
Hilbert
Roots
Norm
Computing

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Ramification Groups of Nonabelian Kummer Extensions. / Sharifi, Romyar T.

In: Journal of Number Theory, Vol. 65, No. 1, 07.1997, p. 105-115.

Research output: Contribution to journalArticle

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