A valuation criterion for normal bases in elementary abelian extensions

2006/04/29 by Nigel P. Byott, Byott, Nigel P., G. Griffith Elder +1
Computer Science · Mathematics · #11S15 #13B05 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11S15 #msc:13B05

paper · pdf · doi:10.48550/arxiv.math/0605011

In addition to some small notational changes, the title "On the valuation of normal basis generators" was changed. The paper is accepted by the Bulletin of the LMS

openalex publication_date 2006/04/29 · arxiv created 2006/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number and let K be a finite extension of the field ℚ_p of p-adic numbers. Let N be a fully ramified, elementary abelian extension of K. Under a mild hypothesis on the extension N/K, we show that every element of N with valuation congruent mod [N:K] to the largest lower ramification number of N/K generates a normal basis for N over K.

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