Galois Groups and Fundamental Groups
Galois Groups and Fundamental Groups
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Galois Groups and Fundamental Groups by Tams Szamuely
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.
"The book is well written and contains much information about the etale fundamental groupThere are exercises in every chapter. On the whole, the book is useful for mathematicians and graduate students looking for one place where they can find information about the etale fundamental group and the related Nori fundamental group scheme." Swaminathan Subramanian, Mathematical Reviews
Tamás Szamuely is a Senior Research Fellow in the Alfréd Rényi Institute of Mathematics at the Hungarian Academy of Sciences, Budapest.
| SKU | Unavailable |
| ISBN 13 | 9780521888509 |
| ISBN 10 | 0521888506 |
| Title | Galois Groups and Fundamental Groups |
| Author | Tamás Szamuely |
| Series | Cambridge Studies In Advanced Mathematics |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Cambridge University Press |
| Year published | 2009-07-16 |
| Number of pages | 282 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |