Central simple algebras and Galois cohomology:
The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev-Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting poin...
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| Format: | E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2017
|
| Ausgabe: | Second edition. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
165 |
| Links: | https://doi.org/10.1017/9781316661277 |
| Zusammenfassung: | The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev-Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev-Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch-Gabber-Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics. |
| Umfang: | 1 Online-Ressource (xi, 417 Seiten) |
| ISBN: | 9781316661277 |
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| 100 | 1 | |a Gille, Philippe |d 1968- | |
| 245 | 1 | 0 | |a Central simple algebras and Galois cohomology |c Philippe Gille, Tamás Szamuely |
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| 490 | 1 | |a Cambridge studies in advanced mathematics |v 165 | |
| 520 | |a The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev-Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev-Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch-Gabber-Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics. | ||
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| spelling | Gille, Philippe 1968- Central simple algebras and Galois cohomology Philippe Gille, Tamás Szamuely Second edition. Cambridge Cambridge University Press 2017 1 Online-Ressource (xi, 417 Seiten) txt c cr Cambridge studies in advanced mathematics 165 The first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields, this book starts from the basics and reaches such advanced results as the Merkurjev-Suslin theorem, a culmination of work initiated by Brauer, Noether, Hasse and Albert, and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, the text covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, and techniques in Milnor K-theory and K-cohomology, leading to a full proof of the Merkurjev-Suslin theorem and its application to the characterization of reduced norms. The final chapter rounds off the theory by presenting the results in positive characteristic, including the theorems of Bloch-Gabber-Kato and Izhboldin. This second edition has been carefully revised and updated, and contains important additional topics. Szamuely, Tamás Erscheint auch als Druck-Ausgabe 9781107156371 Erscheint auch als Druck-Ausgabe 9781316609880 |
| spellingShingle | Gille, Philippe 1968- Central simple algebras and Galois cohomology |
| title | Central simple algebras and Galois cohomology |
| title_auth | Central simple algebras and Galois cohomology |
| title_exact_search | Central simple algebras and Galois cohomology |
| title_full | Central simple algebras and Galois cohomology Philippe Gille, Tamás Szamuely |
| title_fullStr | Central simple algebras and Galois cohomology Philippe Gille, Tamás Szamuely |
| title_full_unstemmed | Central simple algebras and Galois cohomology Philippe Gille, Tamás Szamuely |
| title_short | Central simple algebras and Galois cohomology |
| title_sort | central simple algebras and galois cohomology |
| work_keys_str_mv | AT gillephilippe centralsimplealgebrasandgaloiscohomology AT szamuelytamas centralsimplealgebrasandgaloiscohomology |