On the necessity of new ramification breaks

Nigel P. Byott; G. Griffith Elder

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arXiv · 0704.3951

On the necessity of new ramification breaks

Nigel P. Byott·G. Griffith Elder

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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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Nigel P. Byott, G. Griffith Elder. 2007-04-30. On the necessity of new ramification breaks. https://arxiv.org/abs/0704.3951

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