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