We consider the following general problem: let F be a known field with absolute Galois group GF . Let K be a field with GK ≃ GF . What can be deduced about the arithmetic structure of K? As a prototype of this kind of questions we recall the celebrated Artin–Schreier theorem: GK ≃ GR if and only if K is real closed. Likewise, the fields K with GK ≃ GE for… (More)