The Brauer-Grothendieck group

The Brauer-Grothendieck group / Jean-Louis Colliot-Thélène, Alexei N. Skorobogatov.

This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was...

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Bibliographic Details
Main Authors: Colliot-Thélène, J.-L. (Jean-Louis) (Author), Skorobogatov, Alexei, 1961- (Author)
Format: Book
Language:English
Published: Cham, Switzerland : Springer Nature Switzerland AG, [2021]
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 71.
Subjects:
Grothendieck groups.
Brauer groups.
Schemes (Algebraic geometry)
Cohomology operations.
Table of Contents:
  • Galois Cohomology
  • Étale Cohomology
  • Brauer Groups of Schemes
  • Comparison of the Two Brauer Groups, II
  • Varieties Over a Field
  • Birational Invariance
  • Severi-Brauer Varieties and hypersurfaces
  • Singular Schemes and Varieties
  • Varieties with a Group Action
  • Schemes Over Local Rings and Fields
  • Families of Varieties
  • Rationality in a Family
  • The Brauer-Manin Set and the formal lemma
  • Rational Points in the Brauer-Manin Set
  • The Brauer-Manin Obstruction for Zero-Cycles
  • The Tate Conjecture, Abelian Varieties and K3 Surfaces.

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