GALOIS GROUPS AND FUNDAMENTAL GROUPS by Tamas Szamuely ( 9780511627064 )

Item Details

Title:

GALOIS GROUPS AND FUNDAMENTAL GROUPS

By:

Format:

Electronic book text

List price:	£135.00
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ISBN 10:

0511627068

ISBN 13:

9780511627064

Publisher:

CAMBRIDGE UNIVERSITY PRESS

Pub. date:

5 August, 2012

Series:

Cambridge Studies in Advanced Mathematics 117

Description:

Assuming little technical background, the author presents the strong analogies between these two concepts starting at an elementary level.

Synopsis:

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.

Illustrations:

60 exercises

Publication:

Imprint:

Cambridge University Press (Virtual Publishing)

Returns:

Non-returnable

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GALOIS GROUPS AND FUNDAMENTAL GROUPS (HB)