A valuation criterion for normal bases in elementary abelian extensions

University of Exeter, Exeter, England, United Kingdom
Bulletin of the London Mathematical Society (Impact Factor: 0.7). 05/2006; 39. DOI: 10.1112/blms/bdm036
Source: arXiv

ABSTRACT Let $p$ be a prime number and let $K$ be a finite extension of the field $\mathbb{Q}_p$ 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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Available from: Nigel P. Byott, Jul 16, 2014
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