Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T05:57:25.806Z Has data issue: false hasContentIssue false
  • English
  • Français

RAMIFICATION IN KUMMER EXTENSIONS ARISING FROM ALGEBRAIC TORI

Part of: Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  17 August 2017

MASAMITSU SHIMAKURA Open the ORCID record for MASAMITSU SHIMAKURA [Opens in a new window]
MASAMITSU SHIMAKURA*
Affiliation:
Department of Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku, Tokyo, 162-8601, Japan email 1115704@ed.tus.ac.jp
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe the ramification in cyclic extensions arising from the Kummer theory of the Weil restriction of the multiplicative group. This generalises the classical theory of Hecke describing the ramification of Kummer extensions.

Keywords

local fieldramificationalgebraic tori

MSC classification

Primary: 11S15: Ramification and extension theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 2 , October 2017 , pp. 196 - 204
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

Cohen, H., Advanced Topics in Computational Number Theory, Graduate Texts in Mathematics, 193 (Springer, New York, 2000).CrossRefGoogle Scholar
Fesenko, I. B. and Vostokov, S. V., Local Fields and Their Extensions, 2nd edn, Translations of Mathematical Monographs, 121 (American Mathematical Society, Providence, RI, 2002).Google Scholar
Kida, M., ‘Descent Kummer theory via Weil restriction of multiplicative groups’, J. Number Theory 130(3) (2010), 639–659.CrossRefGoogle Scholar
Komatsu, T., ‘Arithmetic of Rikuna’s generic cyclic polynomial and generalization of Kummer theory’, Manuscripta Math. 114(3) (2004), 265–279.CrossRefGoogle Scholar
Ono, T., ‘Arithmetic of algebraic tori’, Ann. of Math. (2) 74 (1961), 101–139.CrossRefGoogle Scholar