Propagation de la 2-birationalité

Claire Bourbon ¹   ; Jean-François Jaulent ²

¹ Univ. Bordeaux Institut de Mathématiques de Bordeaux 351 Cours de la Libération F-33405 Talence Cedex, France and CNRS Institut de Mathématiques de Bordeaux 351 Cours de la Libération F-33405 Talence Cedex, France
² Université Bordeaux et CNRS Institut de Mathématiques de Bordeaux 351 Cours de la Libération F-33405 Talence Cedex, France and CNRS Institut de Mathématiques de Bordeaux 351 Cours de la Libération F-33405 Talence Cedex, France

Acta Arithmetica, Tome 160 (2013) no. 3, pp. 285-301

Résumé

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.

Détail

DOI : 10.4064/aa160-3-5

Mots-clés : birational cm extension totally real rational number field characterize terms tame ramification totally real extensions compositum still birational extension linearly disjoint cyclotomic mathbb extension prove quadratic furthermore construct infinite towers extensions