The Brauer-Grothendieck-Group

Table of contents:

  • Introduction
    • Diophantine equations, the Hasse principle and the Manin obstruction
    • Content of the project
  • Prerequisites
    • Cohomology
    • Reduced norm and unramied extensions
    • Sites and sheaf cohomology
  • The Brauer group of a field
    • Classical construction of the Brauer group
    • The Brauer group as a H1
    • The Brauer group as a H2
    • The Brauer group of a local field
  • The Brauer-Grothendieck group
    • Azumaya algebra over a local ring and Brauer group of a local ring
    • The Brauer group of a scheme
    • The cohomological Brauer group of a scheme
    • A brief summary
    • Some results

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