Groups As Galois Groups - An Introduction

Klappentext Develops the mathematical background and recent results on the Inverse Galois Problem. Zusammenfassung The goal of this book is to lead the reader to an understanding of recent results on the Inverse Galois Problem. Assuming only elementary algebra and complex analysis! the author develops the necessary background from topology! Riemann surface theory and number theory. Inhaltsverzeichnis Part 1. The Basic Rigidity Criteria: 1. Hilbert's irreducibility theorem; 2. Finite Galois extensions of C (x); 3. Descent of base field and the rigidity criterion; 4. Covering spaces and the fundamental group; 5. Riemann surfaces and their functional fields; 6. The analytic version of Riemann's existence theorem; Part II. Further Directions: 7. The descent from C to k; 8. Embedding problems: braiding action and weak rigidity; Moduli spaces for covers of the Riemann sphere; Patching over complete valued fields.

Produktdetails

• Autoren: Volklein Helmut, Helmut Volklein, Volklein Helmut
• Verlag: Cambridge University Press ELT
• Sprache: Englisch
• Produktform: Taschenbuch
• Erschienen: 12.06.2008
• EAN: 9780521065030
• ISBN: 978-0-521-06503-0
• Seiten: 268
• Serien: Cambridge Studies in Advanced; Cambridge Studies in Advanced Mathematics
• Themen: Naturwissenschaften, Medizin, Informatik, Technik > Naturwissenschaften allgemein; Algebra, MATHEMATICS / Group Theory, MATHEMATICS / Algebra / General, Groups & group theory, Groups and group theory