Galois scaffolds and semistable extensions

2018/11/01 by Keating, Kevin
#11S15 (Primary) 11R33 #11S20 (Secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1811.00630

Abstract

Let K be a local field and let L/K be a totally ramified Galois extension of degree pⁿ. Being semistable and possessing a Galois scaffold are two conditions which facilitate the computation of the additive Galois module structure of L/K. In this note we show that L/K is semistable if and only if L/K has a Galois scaffold. We also give sufficient conditions in terms of Galois scaffolds for the extension L/K to be stable.

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