Inverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory. In all these areas important progress was made in the last few years. The aim of the book is to give a consistent and reasonably complete survey of these results, with the main emphasis on the rigidity method and its applications. Among others the monograph presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems combined with a collection of the existing Galois realizations.

Among others this monograph presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems combined with a collection of the existing Galois realizations. The last chapter gives an introduction to the results on fundamental groups in positive characteristic obtained by rigid analytic methods. Finally, it is supplemented by tables of example polynomials for transitive respectively primitive permutation groups up to degree 30.

Klappentext

Inverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory. In all these areas important progress was made in the last few years. The aim of the book is to give a consistent and reasonably complete survey of these results, with the main emphasis on the rigidity method and its applications. Among others the monograph presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems combined with a collection of the existing Galois realizations.

Inhalt
I. The Rigidity Method.- II. Applications of Rigidity.- III. Action of Braids.- IV. Embedding Problems.- V. Rigid Analytic Methods.