ENGLISH

Galois Groups and Fundamental Groups

By Tamás Szamuely

Book information

Publisher
Cambridge University Press
Year
2009
ISBN
9780521888509, 0521888506
LCC
QA214 .S95 2009
Language
english
Format
PDF
Filesize
2 MB (2332187 bytes)
Series
Cambridge Studies in Advanced Mathematics 117
Edition
1
Pages
280\277
Topic
Education
Time added
2011-06-04 13:46:07

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.

Similar books