Galois groups and fundamental groups:
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 o...
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2009
|
| Schriftenreihe: | Cambridge studies in advanced mathematics
117 |
| Links: | https://doi.org/10.1017/CBO9780511627064 |
| Zusammenfassung: | 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. |
| Umfang: | 1 Online-Ressource (ix, 270 Seiten) |
| ISBN: | 9780511627064 |
Internformat
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| spelling | Szamuely, Tamás Galois groups and fundamental groups Tamás Szamuely Galois Groups & Fundamental Groups Cambridge Cambridge University Press 2009 1 Online-Ressource (ix, 270 Seiten) txt c cr Cambridge studies in advanced mathematics 117 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. Erscheint auch als Druck-Ausgabe 9780521888509 |
| spellingShingle | Szamuely, Tamás Galois groups and fundamental groups |
| title | Galois groups and fundamental groups |
| title_alt | Galois Groups & Fundamental Groups |
| title_auth | Galois groups and fundamental groups |
| title_exact_search | Galois groups and fundamental groups |
| title_full | Galois groups and fundamental groups Tamás Szamuely |
| title_fullStr | Galois groups and fundamental groups Tamás Szamuely |
| title_full_unstemmed | Galois groups and fundamental groups Tamás Szamuely |
| title_short | Galois groups and fundamental groups |
| title_sort | galois groups and fundamental groups |
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