Galois Groups and Fundamental Groups

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Sprache: Englisch

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Beschreibung

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.

Über den Autor

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

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.

Details

Genre:	Importe
Medium:	Buch
Inhalt:	Gebunden
ISBN-13:	9780521888509
ISBN-10:	0521888506
Sprache:	Englisch
Einband:	Gebunden
Autor:	Szamuely, Tamás
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	235 x 157 x 20 mm
Von/Mit:	Tamás Szamuely
Erscheinungsdatum:	26.08.2015
Gewicht:	0,563 kg