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Central Simple Algebras and Galois Cohomology: Cambridge Studies in Advanced Mathematics, cartea 165

Autor Philippe Gille, Tamás Szamuely
en Limba Engleză Paperback – 9 aug 2017
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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Specificații

ISBN-13: 9781316609880
ISBN-10: 131660988X
Pagini: 430
Ilustrații: 80 exercises
Dimensiuni: 152 x 228 x 23 mm
Greutate: 0.58 kg
Ediția:2Revizuită
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Studies in Advanced Mathematics

Locul publicării:Cambridge, United Kingdom

Cuprins

1. Quaternion algebras; 2. Central simple algebras and Galois descent; 3. Techniques from group cohomology; 4. The cohomological Brauer group; 5. Severi–Brauer varieties; 6. Residue maps; 7. Milnor K-theory; 8. The Merkurjev–Suslin theorem; 9. Symbols in positive characteristic; Appendix. A breviary of algebraic geometry; Bibliography; Index.

Descriere

The first comprehensive modern introduction to central simple algebra starting from the basics and reaching advanced results.

Notă biografică