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Note on 2-Rational Fields by Georges Gras; Jean-François Jaulent is a Mathematics article available to read on EtoBox.
What is Note on 2-Rational Fields about?
We give an alternative computation of the Galois group of the maximal 2-ramified and complexified pro-2-extension of any 2rational number field (Theorem 2), a particular case of results of Movahhedi-Nguyen Quang Do. This short Note is motivated by the paper [J. Jossey, Galois 2-extensions unramified outside 2, J. Number Theory 124 (2007) 42-76] and, at this occasion, we bring into focus some classical technics of abelian -ramification which, unfortunately, are often ignored, especially those developed by J.-F. Jaulent with the -adic class field theory, and by G. Gras in his book on class field theory, and which considerably simplify the study of such subjects; for instance, our proof of Theorem 2 generalizes the purpose of Jossey's paper in such a way using a result of Herfort-Zalesskii. This Note is mainly an attempt of clarification about -rationality.
Who reads Note on 2-Rational Fields?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Georges Gras; Jean-François Jaulent
- Publisher
- Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-314X)
- Published
- 2009
- Language
- EN
- Field
- Mathematics (Physical Sciences)