Propagation de la 2-birationalité
Tom 160 / 2013
Acta Arithmetica 160 (2013), 285-301
MSC: Primary 11R37; Secondary 11R11, 11R70.
DOI: 10.4064/aa160-3-5
Streszczenie
Let 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 \mathbb {Z}_2-extension K^c/K, we prove that K'/K is at most quadratic. Furthermore, we construct infinite towers of such 2-extensions.
