Let L/K be a 2-birational CM-extension of a totally real 2-rational number field. We characterize in terms of tame ramification totally real 2-extensions K’/K such that the compositum L’=LK’ is still 2-birational. In case the 2-extension K’/K is linearly disjoint from the cyclotomic ℤ₂-extension , we prove that K’/K is at most quadratic. Furthermore, we construct infinite towers of such 2-extensions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-3-5,
author = {Claire Bourbon and Jean-Fran\c cois Jaulent},
title = {Propagation de la 2-birationalit\'e},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {285-301},
zbl = {1287.11129},
language = {fra},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-3-5}
}
Claire Bourbon; Jean-François Jaulent. Propagation de la 2-birationalité. Acta Arithmetica, Tome 161 (2013) pp. 285-301. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-3-5/