Propagation de la 2-birationalit\'e

TL;DR

This paper studies 2-birational CM-extensions over totally real 2-rational fields, characterizing certain ramified extensions and constructing infinite towers of such extensions.

Contribution

It provides a characterization of tame ramification in 2-birational extensions and constructs infinite towers of these extensions.

Findings

K'/K is at most quadratic when disjoint from the cyclotomic Z2-extension.

Characterization of tame ramification in 2-birational extensions.

Construction of infinite towers of 2-extensions.

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-extensions K'/K is linearly disjoint from the cyclotomic Z2-extension Kc/K, we prove that K'/K is at most quadratic. In the other hand we construct infinite towers of such 2-extensions.