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G. Griffith Elder; Jeffrey J. Hooper
On wild ramification in quaternion extensions
Journal de théorie des nombres de Bordeaux, 19 no. 1 (2007), p. 101-124, doi: 10.5802/jtnb.576
Article PDF | Reviews MR 2332056 | Zbl 1123.11037

Résumé - Abstract

This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain $\sqrt{-1}$ (along with some partial results for the more general case). This catalog depends upon the refined ramification filtration, which as defined in [2] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare and can occur only when the refined ramification filtration is, in two different ways, extreme.

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