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Inverse galois theory / Gunter Malle, B. Heinrich Matzat

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Springer Monographs in Mathematics | Springer eBook Collection | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2018Copyright date: © 2018Edition: Second editionDescription: 1 Online-Ressource (XVII, 533 Seiten)ISBN:
  • 9783662554203
Subject(s): Additional physical formats: 9783662554197 | Erscheint auch als: Inverse galois theory. Online-Ausgabe Second edition. Berlin : Springer, 2018. xvii, 533 SeitenDDC classification:
  • 512.2
MSC: MSC: *12-02 | 12F12 | 12F10 | 12G05 | 14G22RVK: RVK: SK 200LOC classification:
  • QA174-183
DOI: DOI: 10.1007/978-3-662-55420-3Online resources: Summary: 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 equationsSummary: 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 -- IndexPPN: PPN: 102803203XPackage identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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