Galois groups and fundamental groups / Tamás Szamuely.

Format:

Book

Author/Creator:

Szamuely, Tamás, author.

Series:

Cambridge studies in advanced mathematics ; 117.

Cambridge studies in advanced mathematics ; 117

Language:

English

Subjects (All):

Galois theory.

Physical Description:

1 online resource (ix, 270 pages) : digital, PDF file(s).

Other Title:

Galois Groups & Fundamental Groups

Place of Publication:

Cambridge : Cambridge University Press, 2009.

Language Note:

English

Summary:

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.

Contents:

Galois theory of fields

Fundamental groups in topology

Riemann surfaces

Fundamental groups of algebraic curves

Fundamental groups of schemes

Tannakian fundamental groups.

Notes:

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

Includes bibliographical references and index.

ISBN:

1-107-20106-3

1-139-63773-8

0-511-62706-8

0-511-59329-5

0-511-65128-7

0-511-59236-1

0-511-59522-0

OCLC:

609843126