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Unramified Brauer group and its applications

Author: Sergey Gorchinskiy; Constantin Shramov
Publisher: Providence, Rhode Island : American Mathematical Society, [2018] ©2018
Series: Translations of mathematical monographs, v. 246.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
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Document Type: Book
All Authors / Contributors: Sergey Gorchinskiy; Constantin Shramov
ISBN: 9781470440725 1470440725
OCLC Number: 1022980429
Description: xvii, 179 pages : illustrations ; 27 cm.
Contents: Part I . Preliminaries on Galois cohomology --
Chapter 1. Group Cohomology --
Chapter 2. Galois Cohomology --
Part II . Brauer group --
Chapter 3. Brauer Group of a Field --
Chapter 4. Residue Map on a Brauer Group --
Part III . Applications to rationality problems --
Chapter 5. Example of a Unirational Non-rational Variety --
Chapter 6. Arithmetic of Two-dimensional Quadrics --
Chapter 7. Non-rational Double Covers of \Pb³ --
Chapter 8. Weil Restriction and Algebraic Tori --
Chapter 9. Example of a Non-rational Stably Rational Variety --
Part IV . The Hasse principle and its failure --
Chapter 10. Minkowski–Hasse Theorem --
Chapter 11. Brauer–Manin Obstruction --
Series Title: Translations of mathematical monographs, v. 246.
Responsibility: Sergey Gorchinskiy, Constantin Shramov.

Abstract:

Explores arithmetic geometry with special attention given to the unramified Brauer group of algebraic varieties and its most striking applications in birational and Diophantine geometry. Topics  Read more...

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