000			01811 a2200265 4500
999			_c54414 _d54414
008			210324b ||||| |||| 00| 0 eng d
020			_a9781316609880
082			_a514.23 _bGIL
100			_aGille, Philippe
245			_aCentral Simple algebras and Galois cohomology
250			_a2nd
260			_bCambridge University Press, _c2017. _aCambridge:
300			_axii, 343 p. : ill. ; _bpb. ; _c24 cm.
365			_aGBP _b36.99
440			_a Cambridge studies in advanced mathematics; 165
504			_aIncludes bibliographical references (p. [323]-338) and index.
520			_aThe 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.
650			_aAlgebra
650			_aGalois cohomology
650			_aAlgebra, Homological
650			_aAssociative algebras
650			_aQuaternion algebra
700			_aSzamuely, Tamás
942			_2ddc _cTD