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Central Simple Algebras and Galois Cohomology - Philippe Gille, Tamás Szamuely

Central Simple Algebras and Galois Cohomology

Buch | Hardcover
430 Seiten
2017 | 2nd Revised edition
Cambridge University Press (Verlag)
978-1-107-15637-1 (ISBN)
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The first comprehensive, modern introduction to a central field in modern algebra with connections to algebraic geometry, K-theory, and number theory. It proceeds from the basics to more advanced results, including the Merkurjev–Suslin theorem. It is ideal as a text for a graduate course and as a reference for researchers.
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.

Philippe Gille is a Research Director for Centre National de la Recherche Scientifique at Institut Camille Jordan, Lyon. He has written numerous research papers on linear algebraic groups and related structures. Tamás Szamuely is a Research Advisor at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences, Budapest and a Professor at the Central European University, Hungary. He is the author of Galois Groups and Fundamental Groups (Cambridge, 2009), also published in the Cambridge Studies in Advanced Mathematics series, as well as numerous research papers.

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.

Erscheinungsdatum
Reihe/Serie Cambridge Studies in Advanced Mathematics
Zusatzinfo Worked examples or Exercises
Verlagsort Cambridge
Sprache englisch
Maße 158 x 235 mm
Gewicht 720 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 1-107-15637-8 / 1107156378
ISBN-13 978-1-107-15637-1 / 9781107156371
Zustand Neuware
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