A valuation criterion for normal bases in elementary abelian extensions

Details A valuation criterion for normal bases in elementary abelian extensions A valuation criterion for normal bases in elementary abelian extensions

2006-04-29

arxiv.org/abs/math/0605011v2

Mathematics

Number Theory

In addition to some small notational changes, the title "On the valuation of normal basis generators" was changed. The paper i

Scientific paper

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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