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Look Inside Local Cohomology

Local Cohomology
An Algebraic Introduction with Geometric Applications

Part of Cambridge Studies in Advanced Mathematics

Authors:
M. P. Brodmann, Universität Zürich
R. Y. Sharp, University of Sheffield

Date Published: February 2011
availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
format: Adobe eBook Reader
isbn: 9780511831010

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About the Authors

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.
- Gives a detailed and comprehensive account of this material
- Covers important applications
- Uses detailed examples designed to illustrate the geometrical significance of aspects of local cohomology
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Reviews & endorsements
'… a careful and detailed algebraic introduction to Grothendieck's local cohomology theory.' L'Enseignment Mathématique
'The book is well organised, very nicely written, and reads very well … a very good overview of local cohomology theory.' European Mathematical Society
'I am sure that this will be a standard text and reference book for years to come.' Liam O'Carroll, Bull. London Mathematical Society
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Product details
- Date Published: February 2011
- format: Adobe eBook Reader
- isbn: 9780511831010
- contains: 6 b/w illus.
- availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
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.
Look Inside
Authors
M. P. Brodmann, Universität Zürich
R. Y. Sharp, University of Sheffield