Local cohomology : an algebraic introduction with geometric applications

Author(s)

Bibliographic Information

Local cohomology : an algebraic introduction with geometric applications

M.P. Brodmann, R.Y. Sharp

（Cambridge studies in advanced mathematics, 60）

Cambridge University Press, 1998

  • : hardback

Available at  / 69 libraries

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Note

Includes bibliographical references (p. 407-409) and index

Description and Table of Contents

Description

This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and provides many illustrations of applications of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Castelnuovo-Mumford regularity, the Fulton-Hansen connectedness theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. It is designed for graduate students who have some experience of basic commutative algebra and homological algebra, and also for experts in commutative algebra and algebraic geometry.

Table of Contents

  • Preface
  • Notation and conventions
  • 1. The local cohomology functors
  • 2. Torsion modules and ideal transforms
  • 3. The Mayer-Vietoris Sequence
  • 4. Change of rings
  • 5. Other approaches
  • 6. Fundamental vanishing theorems
  • 7. Artinian local cohomology modules
  • 8. The Lichtenbaum-Hartshorne theorem
  • 9. The Annihilator and Finiteness Theorems
  • 10. Matlis duality
  • 11. Local duality
  • 12. Foundations in the graded case
  • 13. Graded versions of basic theorems
  • 14. Links with projective varieties
  • 15. Castelnuovo regularity
  • 16. Bounds of diagonal type
  • 17. Hilbert polynomials
  • 18. Applications to reductions of ideals
  • 19. Connectivity in algebraic varieties
  • 20. Links with sheaf cohomology
  • Bibliography
  • Index.

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