Description: 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.
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EAN: 9780521888509
UPC: 9780521888509
ISBN: 9780521888509
MPN: N/A
Book Title: Galois Groups and Fundamental Groups (Cambridge St
Number of Pages: 282 Pages
Language: English
Publication Name: Galois Groups and Fundamental Groups
Publisher: Cambridge University Press
Subject: Algebra / General
Item Height: 0.7 in
Publication Year: 2009
Type: Textbook
Item Weight: 18.4 Oz
Subject Area: Mathematics
Author: Tamás Szamuely
Item Length: 9 in
Series: Cambridge Studies in Advanced Mathematics Ser.
Item Width: 6 in
Format: Hardcover
