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OverviewFull Product DetailsAuthor: Jean-Louis Colliot-Thélène , Alexei N. SkorobogatovPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2021 Volume: 71 Weight: 0.869kg ISBN: 9783030742478ISBN 10: 3030742474 Pages: 450 Publication Date: 31 July 2021 Audience: Professional and scholarly , College/higher education , Professional & Vocational , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1 Galois Cohomology.- 2 Étale Cohomology.- 3 Brauer Groups of Schemes.- 4 Comparison of the Two Brauer Groups, II.- 5 Varieties Over a Field.- 6 Birational Invariance.- 7 Severi–Brauer Varieties and Hypersurfaces.- 8 Singular Schemes and Varieties.- 9 Varieties with a Group Action.- 10 Schemes Over Local Rings and Fields.- 11 Families of Varieties.- 12 Rationality in a Family.- 13 The Brauer–Manin Set and the Formal Lemma.- 14 Are Rational Points Dense in the Brauer–Manin Set?.- 15 The Brauer–Manin Obstruction for Zero-Cycles.- 16 Tate Conjecture, Abelian Varieties and K3 Surfaces.- Bibliography.- Index.ReviewsThis book has collected in one place much of the fundamental cohomological theory of the Brauer group, along with excellent references. It then gives some coverage of further results, especially on the two important topics of obstructions to rationality and obstructions to the Hasse principle. For whatever is not included in this book, it gives a thorough and coherent overview of the relevant literature. Approximately four hundred references are given. (Thomas Benedict Williams, Mathematical Reviews, September, 2022) “The book gives a comprehensive, clear, up-to date presentation of the theory, including most proofs. A particular strength is that it nicely collects many results, examples and counterexamples from various areas of algebraic and arithmetic geometry … . the book fills a wide gap and is a most welcome addition to the literature.” (Stefan Schröer, zbMATH 1490.14001, 2022) “This book has collected in one place much of the fundamental cohomological theory of the Brauer group, along with excellent references. It then gives some coverage of further results, especially on the two important topics of obstructions to rationality and obstructions to the Hasse principle. For whatever is not included in this book, it gives a thorough and coherent overview of the relevant literature. Approximately four hundred references are given.” (Thomas Benedict Williams, Mathematical Reviews, September, 2022) Author InformationJean-Louis Colliot-Thélène works in arithmetic algebraic geometry. He contributed to the study of rational points and of zero-cycles on rationally connected varieties. This involved the use of torsors and the Brauer–Manin obstruction. He applied results from algebraic K-theory (unramified cohomology) to rationality problems, also in complex algebraic geometry. He is the author of some 150 research papers, many written with various collaborators. Jean-Louis Colliot-Thélène received the Fermat prize and a Grand Prix de l'Académie des Sciences de Paris. Alexei Skorobogatov works in arithmetic algebraic geometry with focus on rational points on algebraic varieties, the Brauer group and the Brauer–Manin obstruction, K3 surfaces and abelian varieties. He is the author of the book Torsors and Rational Points and over 75 research papers. Alexei Skorobogatov is the recipient of a Whitehead prize of the London Mathematical Society. Tab Content 6Author Website:Countries AvailableAll regions |
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