Central Simple Algebras and Galois Cohomology
- Philippe Gille, Centre National de la Recherche Scientifique (CNRS), Paris
- Tamás Szamuely, Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest
This book is the first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields. Starting from the basics, it reaches such advanced results as the Merkurjev-Suslin theorem. This theorem is both the 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, but no homological algebra, the book covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, residue maps and, finally, Milnor K-theory and K-cohomology. The last chapter rounds off the theory by presenting the results in positive characteristic, including the theorem of Bloch-Gabber-Kato. The book is suitable as a textbook for graduate students and as a reference for researchers working in algebra, algebraic geometry or K-theory.Read more
- Modern, comprehensive introduction assuming only a solid background in algebra, but no homological algebra; necessary results from algebraic geometry are summarized in an appendix
- Accessible proof of the Merkurjev-Suslin theorem
- First textbook treatment of characteristic p methods, including the Jacobson-Cartier and Bloch-Gabber-Kato theorems
Reviews & endorsements
'The presentation of material is reader-friendly, arguments are clear and concise, exercises at the end of every chapter are original and stimulating, the appendix containing some basic notions from algebra and algebraic geometry is helpful. To sum up, the book under review can be strongly recommended to everyone interested in the topic.' Zentralblatt MATH
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- Date Published: August 2006
- format: Adobe eBook Reader
- isbn: 9780511223150
- contains: 80 exercises
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
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
Find resources associated with this titleYour search for '' returned .
Type Name Unlocked * Format Size
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact firstname.lastname@example.org.
Sorry, this resource is locked