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A valuation criterion for normal bases in elementary abelian extensions

A valuation criterion for normal bases in elementary abelian extensions Let p be a prime number, and let K be a finite extension of the field ℚp 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

A valuation criterion for normal bases in elementary abelian extensions

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References (8)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bdm036
Publisher site
See Article on Publisher Site

Abstract

Let p be a prime number, and let K be a finite extension of the field ℚp 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.

Journal

Bulletin of the London Mathematical Society – Wiley

Published: Oct 1, 2007

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