Minimality and abyssalite of abeliennes extensions and projectives of Q

作者：Deschamps Bruno^*

来源：Journal of Algebra, 2015, 441: 1-20.

DOI：10.1016/j.jalgebra.2015.04.047

• Inverse Galois theory
• Shafarevich conjecture
• Galois cohomology
• Projective groups

In this article we classify all the minimal projective subfields of Q(ab). We then focus on the existence of a projective abelian extension of Q which contains no minimal projective subfield. Alongside this work we make the link between these issues and the conjectures of Shafarevich, Fried-Volklein and Debes-Deschamps, to propose a simple description of the absolute Galois group of the field of rational numbers.

• 出版日期2015-11-1