The book is a textbook on arithmetic geometry. The exposition is built around the concept of the unramified Brauer group of an algebraic variety. Topics covered in the book include Galois cohomology, Brauer groups, obstacles to stable rationality, arithmetic and...
geometry of quadrics, Weil's restriction of scalars, algebraic tori, an example of a non-rational stable rational variety, Brauer-Manin obstructions. The entire material is divided into relatively simple problems, accompanied by detailed instructions.
For senior students, graduate students, and researchers.
The book is a textbook on arithmetic geometry. The exposition is built around the concept of the unramified Brauer group of an algebraic variety. Topics covered in the book include Galois cohomology, Brauer groups, obstacles to stable rationality, arithmetic and geometry of quadrics, Weil's restriction of scalars, algebraic tori, an example of a non-rational stable rational variety, Brauer-Manin obstructions. The entire material is divided into relatively simple problems, accompanied by detailed instructions.
For senior students, graduate students, and researchers.
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