On norm residue symbols and conductors

Romyar T. Sharifi

doi:10.1006/jnth.2000.2560

On norm residue symbols and conductors

Romyar T. Sharifi

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Using the norm residue symbol and a reciprocity law of Artin and Hasse, we determine the conductors of Kummer extensions of the form K(a, ζ_n)/K(ζ_n) for any unramified extension K of Q_p, element a∈K*, and primitive pⁿth root of unity ζ_n. We are able to do this without more recent and general reciprocity laws, which were needed in earlier proofs of the case K=Q_p.

Original language	English (US)
Pages (from-to)	196-209
Number of pages	14
Journal	Journal of Number Theory
Volume	86
Issue number	2
DOIs	https://doi.org/10.1006/jnth.2000.2560
State	Published - Feb 2001
Externally published	Yes

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jnth.2000.2560

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AB - Using the norm residue symbol and a reciprocity law of Artin and Hasse, we determine the conductors of Kummer extensions of the form K(a, ζn)/K(ζn) for any unramified extension K of Qp, element a∈K*, and primitive pnth root of unity ζn. We are able to do this without more recent and general reciprocity laws, which were needed in earlier proofs of the case K=Qp.

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ER -

On norm residue symbols and conductors

Abstract

ASJC Scopus subject areas

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