Local Cohomology

Zusatztext Review of the first edition: ' a careful and detailed algebraic introduction to Grothendieck's local cohomology theory.' L'Enseignement Mathematique Informationen zum Autor M. P. Brodmann is Emeritus Professor in the Institute of Mathematics at the University of Zurich. R. Y. Sharp is Emeritus Professor of Pure Mathematics at the University of Sheffield. Zusammenfassung This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field. Inhaltsverzeichnis Preface to the First Edition; Preface to the Second Edition; Notation and conventions; 1. The local cohomology functors; 2. Torsion modules and ideal transforms; 3. The MayerVietoris sequence; 4. Change of rings; 5. Other approaches; 6. Fundamental vanishing theorems; 7. Artinian local cohomology modules; 8. The LichtenbaumHartshorne Theorem; 9. The Annihilator and Finiteness Theorems; 10. Matlis duality; 11. Local duality; 12. Canonical modules; 13. Foundations in the graded case; 14. Graded versions of basic theorems; 15. Links with projective varieties; 16. Castelnuovo regularity; 17. Hilbert polynomials; 18. Applications to reductions of ideals; 19. Connectivity in algebraic varieties; 20. Links with sheaf cohomology; Bibliography; Index.

Autorentext
M. P. Brodmann is Emeritus Professor in the Institute of Mathematics at the University of Zurich.

Klappentext
This popular graduate text has been thoroughly revised and updated to incorporate recent developments in the field.

Zusammenfassung
On its original publication, this algebraic introduction to Grothendieck's local cohomology theory was the first book devoted solely to the topic and it has since become the standard reference for graduate students. This second edition has been thoroughly revised and updated to incorporate recent developments in the field.

Inhalt
Preface to the First Edition; Preface to the Second Edition; 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. Canonical modules; 13. Foundations in the graded case; 14. Graded versions of basic theorems; 15. Links with projective varieties; 16. Castelnuovo regularity; 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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