Unramified Brauer Group and Its Applications
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A01=Constantin Shramov
A01=Sergey Gorchinskiy
Author_Constantin Shramov
Author_Sergey Gorchinskiy
Category=PBF
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Product details
- ISBN 9781470440725
- Weight: 535g
- Dimensions: 178 x 254mm
- Publication Date: 30 Sep 2018
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Hardback
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This book is devoted to arithmetic geometry with special attention given to the unramified Brauer group of algebraic varieties and its most striking applications in birational and Diophantine geometry. The topics include Galois cohomology, Brauer groups, obstructions to stable rationality, Weil restriction of scalars, algebraic tori, the Hasse principle, Brauer-Manin obstruction, and etale cohomology. The book contains a detailed presentation of an example of a stably rational but not rational variety, which is presented as series of exercises with detailed hints. This approach is aimed to help the reader understand crucial ideas without being lost in technical details. The reader will end up with a good working knowledge of the Brauer group and its important geometric applications, including the construction of unirational but not stably rational algebraic varieties, a subject which has become fashionable again in connection with the recent breakthroughs by a number of mathematicians.
Sergey Gorchinskiy, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia.
Constantin Shramov, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia.
Constantin Shramov, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia.
