Includes bibliographical references (pages 167-175) and index.
Notes
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 \Pb p3 s -- 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.