Inverse galois theory

• Verfasst von: Malle, Gunter [VerfasserIn]
• Verfasst von: Matzat, Bernd Heinrich [VerfasserIn]
• Titel: Inverse galois theory
• Verf.angabe: Gunter Malle, B. Heinrich Matzat
• Ausgabe: Second edition
• Verlagsort: Berlin, Heidelberg
• Verlag: Springer Berlin Heidelberg
• Jahr: 2018
• Umfang: 1 Online-Ressource (XVII, 533 Seiten)
• Gesamttitel/Reihe: Springer Monographs in Mathematics
• Gesamttitel/Reihe: Springer eBook Collection
• Gesamttitel/Reihe: SpringerLink : Bücher
• ISBN: 978-3-662-55420-3
• DOI: doi:10.1007/978-3-662-55420-3
• Schlagwörter: (s)Galois-Theorie / (s)Inverses Problem
• Datenträger: Online-Ressource
• Sprache: eng
• (Gesamttitel): Springer eBook Collection. Mathematics and Statistics
• Bibliogr. Hinweis: Erscheint auch als : Online-Ausgabe: Malle, Gunter, 1960 - : Inverse galois theory. - Second edition. - Berlin : Springer, 2018. - xvii, 533 Seiten
• RVK-Notation: SK 200
• Sach-SW: Mathematics
• Sach-SW: Group theory
• Sach-SW: Topology
• K10plus-PPN: 102803203X
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

This second edition addresses 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, as well as its finite epimorphic images, generally referred to as the inverse problem of Galois theory. In the past few years, important strides have been made in all of these areas. The aim of the book is to provide a systematic and extensive overview of these advances, with special emphasis on the rigidity method and its applications. Among others, the book presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems, together with a collection of the current Galois realizations. There have been two major developments since the first edition of this book was released. The first is the algebraization of the Katz algorithm for (linearly) rigid generating systems of finite groups; the second is the emergence of a modular Galois theory. The latter has led to new construction methods for additive polynomials with given Galois group over fields of positive characteristic. Both methods have their origin in the Galois theory of differential and difference equations

Abstract

I.The Rigidity Method -- II. Applications of Rigidity -- III. Action of Braids -- IV. Embedding Problems -- V. Additive Polynomials -- VI.Rigid Analytic Methods -- Appendix: Example Polynomials -- References -- Index