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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Galois scaffolding in one-dimensional elementary abelian extensions


Author: G. Griffith Elder
Journal: Proc. Amer. Math. Soc. 137 (2009), 1193-1203
MSC (2000): Primary 11R33, 11S15
Published electronically: October 16, 2008
MathSciNet review: 2465640
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Abstract: A Galois scaffold is defined to be a variant of a normal basis that allows for an easy determination of valuation and thus has implications for the questions of the Galois module structure. We introduce a class of elementary abelian $ p$-extensions of local function fields of characteristic $ p$, which we call one-dimensional and which should be considered no more complicated than cyclic degree $ p$ extensions, and show that they, just as cyclic degree $ p$ extensions, possess a Galois scaffold.


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Additional Information

G. Griffith Elder
Affiliation: Department of Mathematics, University of Nebraska at Omaha, Omaha, Nebraska 68182-0243
Email: elder@unomaha.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09710-4
PII: S 0002-9939(08)09710-4
Keywords: Ramification, Galois module structure
Received by editor(s): May 17, 2007
Received by editor(s) in revised form: July 21, 2007, September 12, 2007, and April 8, 2008
Published electronically: October 16, 2008
Additional Notes: The author was partially supported by National Science Foundation Grant No. 201080.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.