On the necessity of new ramification breaks

2007/04/30 by Nigel P. Byott, Byott, Nigel P., G. Griffith Elder +1
Computer Science · Mathematics · #11S15 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.NT #msc:11S15

paper · pdf · doi:10.48550/arxiv.0704.3951

arxiv created 2007/04/30 · openalex publication_date 2007/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Ramification invariants are necessary, but not in general sufficient, to determine the Galois module structure of ideals in local number field extensions. This insufficiency is associated with elementary abelian extensions, where one can define a refined ramification filtration -- one with more ramification breaks [JNTB 17 (2005)]. The first refined break number comes from the usual ramification filtration and is therefore necessary. Here we study the second refined break number.

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