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Local Cohomology: An Algebraic Introduction with Geometric Applications
     

Local Cohomology: An Algebraic Introduction with Geometric Applications

by M. P. Brodmann, R. Y. Sharp
 

ISBN-10: 0521372860

ISBN-13: 9780521372862

Pub. Date: 03/28/1998

Publisher: Cambridge University Press

This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and illustrates many applications for 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,

Overview

This book provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, and illustrates many applications for 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.

Product Details

ISBN-13:
9780521372862
Publisher:
Cambridge University Press
Publication date:
03/28/1998
Series:
Cambridge Studies in Advanced Mathematics Series , #60
Edition description:
New Edition
Pages:
436
Product dimensions:
5.98(w) x 8.98(h) x 1.22(d)

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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