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Unramified Brauer Group and Its Applications

About this Title

Sergey Gorchinskiy, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia and Constantin Shramov, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Publication: Translations of Mathematical Monographs
Publication Year: 2018; Volume 246
ISBNs: 978-1-4704-4072-5 (print); 978-1-4704-4857-8 (online)
DOI: https://doi.org/10.1090/mmono/246
MathSciNet review: MR3837107
MSC: Primary 14F22; Secondary 11S85, 12G05, 14E08, 14G05, 14M20, 16K50

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Table of Contents

Front/Back Matter

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Preliminaries on Galois cohomology

• Group Cohomology
• Galois Cohomology

Brauer group

• Brauer Group of a Field
• Residue Map on a Brauer Group

Applications to rationality problems

• Example of a Unirational Non-rational Variety
• Arithmetic of Two-dimensional Quadratics
• Non-rational Double Covers of $\mathbb {P}^3$
• Weil Restriction and Algebraic Tori
• Example of a Non-rational Stably Rational Variety

Hasse principle and its failure

• Minkowski-Hasse Theorem
• Brauer-Manin Obstruction
• Étale Cohomology

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