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Cohomology groups and genera of higher-dimensional fields

About this Title

Ernst Snapper

Publication: Memoirs of the American Mathematical Society
Publication Year: 1957; Number 28
ISBNs: 978-0-8218-1228-0 (print); 978-0-8218-9970-0 (online)
DOI: https://doi.org/10.1090/memo/0028
MathSciNet review: 0095172

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Table of Contents

Chapters

  • Introduction
  • 1. Direct and inverse limits
  • 2. Regular mappings and sheaf homomorphisms
  • 3. Transitive systems of sheaves and their limits
  • 4. Transitive systems and their cohomology groups
  • 5. Exact sequences of transitive systems
  • 6. Exact cohomology sequences for transitive systems
  • 7. The Zariski topology
  • 8. The sheaf of local rings
  • 9. The transitive system of projective models
  • 10. The Riemann manifold
  • 11. The sheaf of valuation rings, cohomology groups and genera ofE
  • 12. The sheaf of valuation rings as limit of the transitive system of projective models
  • 13. Affine models
  • 14. Affine models under birational transformations
  • 15. Cohomology groups under birational transformations
  • 16. The class Ct
  • 17. Cohomology groups under normalization
  • 18. The geometric genus of E/K
  • 19. Subvarieties
  • 20. The map induced by a place
  • 21. The exact cohomology sequence, associated with a place