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Galois groups and fundamental groups

Szamuely, Tamas.

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Galois groups and fundamental groups

Record Type:	Electronic resources : Monograph/item
Title/Author:	Galois groups and fundamental groups/ Tamas Szamuely.
remainder title:	Galois Groups & Fundamental Groups
Author:	Szamuely, Tamas.
Published:	Cambridge :Cambridge University Press, : 2009.,
Description:	ix, 270 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
[NT 15003449]:	Galois theory of fields -- Fundamental groups in topology -- Riemann surfaces -- Fundamental groups of algebraic curves -- Fundamental groups of schemes -- Tannakian fundamental groups.
Subject:	Galois theory. -
Online resource:	https://doi.org/10.1017/CBO9780511627064
ISBN:	9780511627064

Galois groups and fundamental groups
Szamuely, Tamas.

Galois groups and fundamental groups[electronic resource] /Galois Groups & Fundamental GroupsTamas Szamuely. - Cambridge :Cambridge University Press,2009. - ix, 270 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;117. - Cambridge studies in advanced mathematics ;117..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Galois theory of fields -- Fundamental groups in topology -- Riemann surfaces -- Fundamental groups of algebraic curves -- Fundamental groups of schemes -- Tannakian fundamental groups.

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.

ISBN: 9780511627064Subjects--Topical Terms:

523821
Galois theory.

LC Class. No.: QA214 / .S95 2009

Dewey Class. No.: 512.32

Galois groups and fundamental groups
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100 1 $a Szamuely, Tamas. $3 745292
245 1 0 $a Galois groups and fundamental groups $h [electronic resource] / $c Tamas Szamuely.
246 3 $a Galois Groups & Fundamental Groups
260 $a Cambridge : $b Cambridge University Press, $c 2009.
300 $a ix, 270 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 117
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a Galois theory of fields -- Fundamental groups in topology -- Riemann surfaces -- Fundamental groups of algebraic curves -- Fundamental groups of schemes -- Tannakian fundamental groups.
520 $a 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.
650 0 $a Galois theory. $3 523821
830 0 $a Cambridge studies in advanced mathematics ; $v 117. $3 3470686
856 4 0 $u https://doi.org/10.1017/CBO9780511627064