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

 

An ultrametric space of Eisenstein polynomials and ramification theory


Author: Manabu Yoshida
Journal: Proc. Amer. Math. Soc. 140 (2012), 4141-4151
MSC (2010): Primary 11S15; Secondary 11S05
Published electronically: April 25, 2012
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Abstract: We give a criterion whether given Eisenstein polynomials over a local field $ K$ define the same extension over $ K$ in terms of a certain non-Archimedean metric on the set of polynomials. The criterion and its proof depend on ramification theory.


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Additional Information

Manabu Yoshida
Affiliation: Graduate School of Mathematics, Kyushu University, Fukuoka 819-0395, Japan
Email: m-yoshida@math.kyushu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11399-1
PII: S 0002-9939(2012)11399-1
Received by editor(s): June 3, 2011
Published electronically: April 25, 2012
Additional Notes: The author is supported by the Japan Society for the Promotion of Scientist Fellowships for Young Scientists.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2012 American Mathematical Society