Unramified Brauer Group and Its Applications
2018年9月 · Translations of Mathematical Monographs 第 246 本图书 · American Mathematical Soc.
电子书
200
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关于此电子书
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 étale 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.
作者简介
Sergey Gorchinskiy: Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia,
Constantin Shramov: Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
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