Propagation de la 2-birationalité

Volume 160 / 2013

Claire Bourbon, Jean-François Jaulent 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.

Authors

  • Claire BourbonUniv. 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
    e-mail
  • Jean-François JaulentUniversité 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
    e-mail

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