Galois Groups and Fundamental Groups

Erscheinungsjahr 2015
ISBN: 978-0-521-88850-9
Verlag: Cambridge University Press

Buch, Englisch, Band 117, 280 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 563 g

Reihe: Cambridge Studies in Advanced Mathematics

Ever since the concepts of Galois groups in algebra and fundamental groups in topology emerged during the nineteenth century, mathematicians have known of the strong analogies between the two concepts. This book presents the connection starting at an elementary level, showing how the judicious use of algebraic geometry gives access to the powerful interplay between algebra and topology that underpins much modern research in geometry and number theory. Assuming as little technical background as possible, the book starts with basic algebraic and topological concepts, but already presented from the modern viewpoint advocated by Grothendieck. This enables a systematic yet accessible development of the theories of fundamental groups of algebraic curves, fundamental groups of schemes, and Tannakian fundamental groups. The connection between fundamental groups and linear differential equations is also developed at increasing levels of generality. Key applications and recent results, for example on the inverse Galois problem, are given throughout.

Autoren/Hrsg.

Szamuely, Tamás

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Foreword
1. Galois theory of fields
2. Fundamental groups in topology
3. Riemann surfaces
4. Fundamental groups of algebraic curves
5. Fundamental groups of schemes
6. Tannakian fundamental groups
Bibliography
Index.

Über Autor(innen)

Szamuely, Tamás
Tamás Szamuely is a Senior Research Fellow in the Alfréd Rényi Institute of Mathematics at the Hungarian Academy of Sciences, Budapest.