The Brauer-Grothendieck Group (Hardcover, 2021)

1 Galois Cohomology.- 2 Etale 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.