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

Files:

• Main file
• The poster
• Slides of the oral presentation

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…