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 MerkurjevSuslin 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 SeveriBrauer varieties and techniques in Milnor K-theory and K-cohomology leading to a full proof of the MerkurjevSuslin 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 BlochGabberKato and Izhboldin. This second edition has been carefully revised and updated and contains important additional topics.