Galois Groups and Fundamental Groups (Hardcover)
 
作者: Tamas Szamuely 
分類: Algebra ,
Number theory  
書城編號: 388965


售價: $812.00

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出版社: Cambridge University Press
出版日期: 2009/07/16
尺寸: 235x159x19mm
重量: 520 grams
ISBN: 9780521888509
 
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商品簡介
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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